TEST BANK for College Algebra 5th Edition by Cynthia Young

TEST BANK for College Algebra 5th Edition by Cynthia Young

Chapter 1-9

Chapter 1 1.1

Equations and Inequalities

Linear Equations

1) Solve the equation.

-56x - 54 = 10 - 60x A) 16 B) 64 C) -116 D) 60 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

2) Solve the equation.

25c + 2 = 7 + 22c A) 9/47 B) 38 C) 5/3 D) 56 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

3) Solve the equation.

5(x - 3) - 5 = x - 3(x - 2) A) 7/26 B) 6/7 C) 26/7 D) 7/6 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

1

4) Solve the equation. =

+5

A) -5/4 B) -1/9 C) -9 D) -150/19 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

5) Specify the values that must be excluded from the solution set.

-1= A) 0 and 9 B) 9 C) 0 D) -9 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve rational equations that are reducible to linear equations.

6) Specify the values that must be excluded from the solution set.

-

=

A) -20 B) -7 and 20 C) 7 and -20 D) 7, 23, and -20 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve rational equations that are reducible to linear equations.

2

7) Specify the values that must be excluded from the solution set.

-

=

A) -26 B) 26 and -19/8 C) -26 and 8/19 D) -26, 25 and 8/19 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve rational equations that are reducible to linear equations.

8) Specify the values that must be excluded from the solution set. = -9

A) 0 and 29 B) 0 C) 29 D) -9 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve rational equations that are reducible to linear equations.

9) Solve the equation. =5A) 75/29 B) 21/75 C) 29/75 D) 4/5 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve rational equations that are reducible to linear equations.

3

10) Solve the equation. = A) no solution B) 19/20 C) 21/20 D) 1/20 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve rational equations that are reducible to linear equations.

11) Solve the equation. = A) 1/5 B) 5 C) -5 D) -1/5 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve rational equations that are reducible to linear equations.

12) Solve the equation. =6

A) 1 B) 10 C) 5 D) None of the above Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve rational equations that are reducible to linear equations.

13) Solve 2n + 10= 17- 5n.

Answer: 1 Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

4

14) Solve

=

- 140.

Answer: -100 Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

15) Specify any values that must be excluded from the solution set and then solve the equation. =2

Answer: Exclude {0, 1/17}, the solution set is {1/51} or x = 1/51 Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve rational equations that are reducible to linear equations.

16) Solve.

38 - [8 + 12x - 15(x + 5)] = 3(6x + 11) - [8(4x - 1) + 2 - 19x] Answer: 41 Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

17) When traveling in London, Florence decided to check her e-mail at an internet café. There was a flat charge of $3.00 plus a charge of 19 cents a minute. How many minutes was she logged on if her bill was $5.85?

Answer: 15 minutes Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

18) Solve -8z = -80 for z.

A) 10 B) 640 C) -88 D) -72 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

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19) Solve -12u = -3 for u.

A) 4 B) 36 C) D) -9 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

20) Solve -8w - 8 = 64 for w.

A) 80 B) -9 C) 48 D) 72 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

21) Solve

x=-

x + 9 for x.

A) -12 B) C) 12 D) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

22) The perimeter, P, of a rectangle is the distance around it, and can be found by solving the formula P = 2l + 2w, where l is the length and w is the width. What is the length of a rectangle whose perimeter is 30 inches and whose width is 3 inches?

A) 15 inches B) 12 inches C) 24 inches D) 10 inches Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

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23) Solve 7q = 56 for q.

Answer: q = 8 Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

24) The perimeter, P, of a rectangle is the distance around it, and can be found by solving the formula where l is the length and w is the width. What is the length of a rectangle whose perimeter is 102 inches and whose width is 23 inches?

Answer: 28 inches Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

25) The area, A, of a rectangle is the amount of two-dimensional space it takes up and can be found by solving the formula where l is the length and w is the width. What is the length of a rectangle whose area is 80 square inches and whose width is 8 inches?

A) 72 inches B) 64 inches C) 8 inches D) 10 inches Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 01 Learning Objective: Solve linear equations in one variable.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

7

College Algebra, 5e (Young) Chapter 1 Equations and Inequalities 1.2

Applications Involving Linear Equations

1) Juan uses a 10% off total purchase coupon at his local supermarket. His checkout price before tax is $103.75. How much would he have paid without the coupon?

A) $126.81 B) $115.28 C) $125.28 D) $115.38 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

2) Lucas, Rebecca, and Brandon order a large pizza. They decide to split the cost according to how much they will eat. Brandon pays $2.32, Rebecca eats 1/6 of the pizza, and Lucas eats 4/7 of the pizza. How much did the pizza cost?

A) $8.86 B) $0.61 C) $4.06 D) $1.58 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

3) A college bookstore marks up the price it pays the publisher for a book by 25%. If the selling price of a book is $82, how much did the bookstore pay for the book?

A) $102.50 B) $20.50 C) $328.00 D) $65.60 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

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4) A builder of tract homes reduced the price of a model by 15%. If the new price is $167,170, what was its original price?

A) $167,170.15 B) $196,670.59 C) $142,094.50 D) $192,245.50 Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

5) A company has a total of $11,750 allocated for monthly costs. Fixed costs are $6650 a month and variable costs are $13 per unit. How many units can be manufactured a month?

A) 904 B) 512 C) 392 D) 1415 Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

6) Lacie decides to start a small business making monogrammed towels. She can set aside $4670 for monthly costs. Fixed costs are $1800 per month and variable costs are $4 per set of towels.

How many sets of towels can she afford to make per month?

A) 1617 B) 1167 C) 450 D) 717 Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

7) Find the perimeter of a triangle if one side is 35 feet, another side is 1/4 of the perimeter, and the third side is 1/3 of the perimeter. Round your answer to 2 decimal places.

A) 35.58 feet B) 84.00 feet C) 20.42 feet D) 105 feet Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve geometry problems.

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8) The length of a rectangle is 9 more feet than 4 times its width. The perimeter of the rectangle is 358 feet. What is the length of the rectangle?

A) 145 feet B) 94 feet C) 143 feet D) 90 feet Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve geometry problems.

9) William has $14,550 to invest and decides to put some in a CD that earns 2.25% interest per year and the rest in a low risk stock that earns 3.4%. How much did he invest to earn $395.225 interest in the first year?

A) $6995.13 at 2.25% and $7554.87 at 3.4% B) $5900 at 2.25% and $8650 at 3.4% C) $8650 at 2.25% and $5900 at 3.4% D) $7554.87 at 2.25% and $6995.13 at 3.4% Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve interest problems.

10) BJ bought ham and cheese at the deli. The ham costs $6.50 per pound and the cheese costs $4.90 per pound. In total, BJ bought 7.6 pounds and the price was $40.6. How many pounds of each did BJ buy?

A) 2.10 pounds of ham and 5.5 pounds of cheese B) 5.5 pounds of ham and 2.10 pounds of cheese C) 3.56 pounds of ham and 3.56 pounds of cheese D) 6.83 pounds of ham and 0.77 pounds of cheese Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

11) A motorboat can maintain a constant speed of 12 miles per hour relative to the water. The boat makes a trip upstream in 42 minutes and the return trip takes 21 minutes. What is the speed of the current?

A) 0.3 mph B) 12 mph C) 4.0 mph D) 24 mph Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve distance-rate-time problems.

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12) Lee can mow a lawn in 10 minutes. It takes Ito 60 minutes to mow a lawn of the same size.

How long would it take them to mow the lawn if they work together?

A) 35.0 minutes B) 50 minutes C) 8.6 minutes D) 70 minutes Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

13) Aleshia's test scores are 76, 83, 95, and 89. The final will count as two tests. What score does Aleshia need on the final to have an average score of 80?

A) 28.5 B) 68.5 C) 57 D) 80 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

14) A college bookstore marks up the price it pays the publisher for a book by 23%. If the selling price of the book is $107.01, how much did the bookstore pay for the book?

Answer: $87 Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

15) The length of a rectangle is 4 feet more than 4 times its width. The perimeter of the rectangle is 148 feet. What is the length of the rectangle?

Answer: 60 feet Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve geometry problems.

16) The Parsons budgeted $147.00 to landscape their yard with trees and shrubs. Trees each cost $16.50 and shrubs each cost $9.50. Combined they planted a total of 14 trees and shrubs. How many of each did they plant in their yard?

Answer: 2 trees, and 12 shrubs Diff: 3 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve mixture problems.

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17) For a certain experiment, a student requires 20 mL of a solution that is 11% HCl (hydrochloric acid). The store-room has only solutions that are 8% HCl and 12% HCl. How many milliliters of each available solution should be mixed to get 20 mL of 11% HCl? Answer: 5 mL of 8% HCl and 15 mL of 12% HCl solutions Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve mixture problems.

18) An investor has $16,300 to split between two investments. The first investment earns a return of 4.2% annually and the second investment earns a return of 3.6% annually. If the total gain on the investment in the first year is $601.20, how much was put into each investment? (Assume the full $16,300 was invested.)

Answer: Investment 1: $2,400 Investment 2: $13,900 Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve mixture problems.

19) A jogger and a walker travel the same distance. The jogger finishes in 44 minutes. The walker takes 77 minutes. How fast is each exerciser moving if the jogger runs 3 miles per hour faster than the walker?

Answer: Jogger 7 mph Walker 4 mph Diff: 2 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve distance-rate-time problems.

20) Find a number such that 22 less than

the number is

the number.

Answer: 84 Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

21) Find two consecutive odd integers such that the sum of the integers is equal to 41 less than 5 times the larger integer.

Answer: 11 and 13 Diff: 1 Var: 1 Chapter/Section: Ch 01, Sec 02 Learning Objective: Solve application problems involving common formulas.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

College Algebra, 5e (Young) 12

Chapter 2 2.1

Graphs

Basic Tools: Cartesian Plane, Distance, and Midpoint

1) Name the quadrant for the point (-15, -31).

A) I B) II C) III D) IV Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

2) Name the quadrant for the point (-42, 16).

A) I B) II C) III D) IV Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

3) Name the quadrant for the point (19, -38).

A) I B) II C) III D) IV Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

4) Describe the line containing the points (-49, -42), (-18, -42), (45, -42).

A) vertical line B) horizontal line C) a line slanting upward from left to right D) a line slanting downward from left to right Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

13

5) Describe the line containing the points (-17, -27), (-17, 9), (-17, 31).

A) vertical line B) horizontal line C) a line slanting upward from left to right D) a line slanting downward from left to right Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

6) Describe the line containing the points (-22, -33), (18, 33), (37, 46).

A) vertical line B) horizontal line C) a line slanting upward from left to right D) a line slanting downward from left to right E) None of the above.

Answer: E Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

7) Describe the line containing the points (-20, -35), (-16, -77), (-8, -101).

A) vertical line B) horizontal line C) a line slanting upward from left to right D) a line slanting downward from left to right Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

8) Find the distance between the points (1, -7) and (8, -1).

A) B) 85 C) 13 D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Calculate the distance between two points.

14

9) Find the distance between the points (-6, 4) and (-3, 6).

A) B) C) 5 D) 13 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Calculate the distance between two points.

10) Find the midpoint of the segment joining the points (-9, -6) and (-7, -2) A) (-4, -8) B) (-1, -2) C) (-8, -4) D) (-16, -8) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Find the midpoint of a line segment joining two points.

11) Find the midpoint of the segment joining the points (-10, 4) and (9, -7).

A) (-1, -3) B) (-0.5, -1.5) C) (9.5, -5.5) D) (-9.5, 5.5) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Find the midpoint of a line segment joining two points.

12) Calculate the distance (to two decimal places) and the midpoint between the segment joining the points (-2, 2) and (-10, 4).

Answer: distance 8.25, midpoint (-6, 3) Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Calculate the distance between two points.; Find the midpoint of a line segment joining two points.

13) Calculate the distance (to two decimal places) and the midpoint between the segment joining the points (-2.5, 5) and (7.6, 7.4).

Answer: distance 10.38, midpoint (2.55, 6.20) Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Calculate the distance between two points.; Find the midpoint of a line segment joining two points.

15

14) Determine whether the triangle with the given vertices is a right triangle, an isosceles triangle, neither, or both. (Recall that a right triangle satisfies the Pythagorean theorem and an isosceles triangle has at least two sides of equal length.)

(13, 8), (18, -4), and (25, 3) Answer: isosceles triangle Diff: 3 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Calculate the distance between two points.

15) Determine whether the triangle with the given vertices is a right triangle, an isosceles triangle, neither, or both. (Recall that a right triangle satisfies the Pythagorean theorem and an isosceles triangle has at least two sides of equal length.)

(-2, -5), (2, -5), and (2, -1) Answer: right triangle Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Calculate the distance between two points.

16) Give the coordinates for the point in the graph.

Answer: (1, -4) Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

16

17) Give the coordinates for the point in the graph.

A) (3, -4) B) (3, 4) C) (-3, 4) D) (-3, -4) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

18) Give the coordinates for the point in the graph.

Answer: (0, -2) Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

17

19) Give the coordinates for the point in the graph.

A) (0, -3) B) (3, 0) C) (-3, 0) D) -3 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Plot points on the Cartesian plane.

20) Calculate (to two decimal places) the perimeter of the triangle with the following vertices at points A, B, and C.

Answer: 18.39 Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Calculate the distance between two points.

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21) Calculate (to two decimal places) the perimeter of the triangle with the following vertices at points A, B, and C.

A) 11.10 B) 16.22 C) 88.00 D) -0.83 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Calculate the distance between two points.

22) Find the distance between the points (-14, -7) and (-2, -2).

Answer: 13 Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Calculate the distance between two points.

23) Find the distance between the points and Answer: Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 01 Learning Objective: Calculate the distance between two points.

. (Give the exact answer.)

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

College Algebra, 5e (Young) Chapter 2 Graphs 19

2.2

Graphing Equations: Point-Plotting, Intercepts, and Symmetry

1) Determine which point lies on the graph of the equation y = -10 - 4x + 8.

A) (-222, 5) B) (-222, -222) C) (-262, 5) D) (5, -262) Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Sketch graphs of equations by plotting points.

2) Determine which point lies on the graph of the equation y = + 7.

A) (17, 3) B) (3, 17) C) (3, 11) D) (0, 0) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Sketch graphs of equations by plotting points.

3) Which of the following applies to the graph y =

?

A) symmetry with respect to the x-axis B) symmetry with respect to the y-axis C) symmetry with respect to the origin D) no symmetry Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

4) Which of the following applies to the graph 49 + = 25?

A) symmetry with respect to the x-axis B) symmetry with respect to the y-axis C) symmetry with respect to the origin D) no symmetry Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

5) Which of the following applies to the graph y = 5 A) symmetry with respect to the x-axis 20

?

B) symmetry with respect to the y-axis C) symmetry with respect to the origin D) no symmetry Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

6) The point (-17, 18) lies on the graph that is symmetric about the x-axis. State the other point that must also lie on the graph.

A) (17, 18) B) (17, -18) C) (-17, -18) D) (18, -17) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

7) The point (1, -8) lies on the graph that is symmetric about the x-axis. State the other point that must also lie on the graph.

A) (1, 8) B) (-1, -8) C) (-1, 8) D) (-8, 1) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

8) The point (7, -5) lies on the graph that is symmetric about the y-axis. State the other point that must also lie on the graph.

A) (-5, 7) B) (7, 5) C) (-7, -5) D) (-7, 5) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

21

9) The point (-2, -10) lies on the graph that is symmetric about the y-axis. State the other point that must also lie on the graph.

A) (-10, -2) B) (2, -10) C) (-2, 10) D) (2, 10) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

10) The point (-10, 2) lies on the graph that is symmetric about the origin. State the other point that must also lie on the graph.

A) (2, -10) B) (10, 2) C) (-10, -2) D) (10, -2) Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

11) The point (-7, -3) lies on the graph that is symmetric about the origin. State the other point that must also lie on the graph.

A) (-3, -7) B) (7, 3) C) (7, -3) D) (-7, 3) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

12) Use algebraic tests to determine whether the graph of the equation y = 10 + 5 is symmetric with respect to the x-axis, y-axis, or origin.

A) x-axis B) y-axis C) origin D) no symmetry Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

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13) Use algebraic tests to determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, or origin.

A) x-axis B) y-axis C) origin D) x-axis, y-axis, origin Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

14) Use algebraic tests to determine whether the graph of the equation is symmetric with respect to the x-axis, y-axis, or origin.

A) y-axis B) x-axis C) origin D) no symmetry Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

15) The given point (-2, 3) lies on the graph that is symmetric about the x-axis, y-axis, and origin.

State the other points that must also lie on the graph.

Answer: (-2, -3), (2, 3), (2, -3) Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

16) Use algebraic tests to determine whether the graph 5 + 4 = 1 is symmetric with respect to the x-axis, y-axis, or origin.

Answer: x-axis, y-axis, and origin Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

17) Use algebraic tests to determine whether the graph of y = 8 - 6x is symmetric with respect to the x-axis, y-axis, or origin.

Answer: origin Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Conduct a test for symmetry about the x-axis, y-axis, and origin.

23

18) Plot the graph of the given equation. y=1A)

B)

C)

24

D)

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Use intercepts and symmetry as graphing aids.

25

19) The profit associated with making a particular product is given by the equation y = - + 10x - 21 where y represents the profit in millions of dollars and x represents the number of thousands of units sold. corresponds to 1000 units and corresponds to $1M.) Graph this equation and determine how many units must be sold to break even Determine the range of units sold that correspond to making a profit.

A)

3000 units or 7000 units must be sold to break even range of units sold that correspond to making a profit is 3000 to 7000 B)

3000 units or 7000 units must be sold to break even range of units sold that correspond to making a profit is 3000 to 7000 C)

3000 units or 7000 units must be sold to break even range of units sold that correspond to making a profit is from 0 to 3000 or at least 7000 26

D)

3000 units or 7000 units must be sold to break even range of units sold that correspond to making a profit is from 0 to 3000 or at least 7000 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Use intercepts and symmetry as graphing aids.

20) Use symmetry to help you graph the equation.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Use intercepts and symmetry as graphing aids.

27

21) Use symmetry to help you graph the equation.

A)

B)

C)

D)

28

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Use intercepts and symmetry as graphing aids.

29

22) Use symmetry to help you graph the equation.

A)

B)

C)

D)

30

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Use intercepts and symmetry as graphing aids.

31

23) Use symmetry to help you graph the equation.

A)

B)

C)

D)

32

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Use intercepts and symmetry as graphing aids.

24) Match the graph with the corresponding symmetry.

A) Symmetry with respect to the x-axis B) No symmetry C) Symmetry with respect to the y-axis D) Symmetry with respect to the x-axis, y-axis, and origin E) Symmetry with respect to the origin Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Use intercepts and symmetry as graphing aids.

25) Complete the table for the given equation. x y = 5x - 4 (x, y) -6 -4 -2 0 Answer: x -6 -4 -2 0

y = 5x - 4 -34 -24 -14 -4

(x, y) (-6, -34) (-4, -24) (-2, -14) (0, -4)

Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Sketch graphs of equations by plotting points.

33

26) Complete the table for the given equation. y= x (x, y) -3 0 5 12 Answer: x -3 0 5 12

y= 1 2 3 4

(x, y) (-3, 1) (0, 2) (5, 3) (12, 4)

Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Sketch graphs of equations by plotting points.

27) Find the x-intercept(s).

3x + 2y = 6 Answer: x = 2 (2, 0) Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Find intercepts for graphs of equations.

28) Find the y-intercept(s).

-5x + 3y = 9 Answer: y = 3 (3, 0) Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Find intercepts for graphs of equations.

34

29) Find the x-intercept(s). y= - 7x + 10 Answer: x = 2, x = 5 (2, 0) and (5, 0) Diff: 1 Var: 1 Chapter/Section: Ch 02, Sec 02 Learning Objective: Find intercepts for graphs of equations.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

35

College Algebra, 5e (Young) Chapter 3 Functions and Their Graphs 3.1

Functions

1) Classify the following relationship as a function or not a function. {(-17, 20), (17, 20), (-12, 20), (1, 20)} A) a function B) not a function C) don't know Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether a relation is a function.

2) Classify the following relationship as a function or not a function. {(9, -18), (9, -2), (9, 15), (9, -3)} A) a function B) not a function C) don't know Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether a relation is a function.

3) Classify the following relationship as a function or not a function. {(15, 10), (-10, -20), (-20, -16), (-14, 1), (-12, -14)} A) a function B) not a function C) don't know Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether a relation is a function.

4) Classify the following relationship as a function or not a function. {(4, 10), (18, -2), (12, 2), (4, 16)} A) a function B) not a function C) don't know Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether a relation is a function.

36

5) Determine if the equation x = is a function.

A) a function B) not a function C) don't know Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether an equation represents a function.

6) Determine if the equation 8 + 4 = 4 is a function.

A) a function B) not a function C) don't know Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether an equation represents a function.

7) Determine if the equation x = is a function with independent variable x and dependent variable y.

A) a function B) not a function C) don't know Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether an equation represents a function.

8) Given the function f (x) = 5x - 4, evaluate f (x + 10).

A) 5x + 46 B) 5x - 46 C) 5 + 46 D) 5x + 6 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.; Use function notation.

37

9) Given the function f (x) = - 3x + 2, evaluate f (x) - f (6).

A) - 3x + 18 B) - 3x - 20 C) - 3x - 18 D) x - 6 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.; Use function notation.

10) Given the function H(x) = 1 A) -4 B) -4 + 10x -

, evaluate H(x - 5).

C) -24 + 7x D) -4 - x Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.; Use function notation.

11) Given the function G(x) = 6 - 4x, evaluate G(4x + 2).

A) -16 + 16x + 12 B) -16 + 2 C) -16x - 14 D) -16x - 2 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.; Use function notation.

12) Given the function G(x) = -7 - 6x, evaluate G(4).

A) 17 B) 31 C) -31 D) 4x - 7 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.

38

13) Given the function f (x) =

- 5x - 15, evaluate

.

A) 2x + h - 5 B) C) 2x + h + 5 D) 1 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.

14) Given the function f (x) = -7 - 5x, evaluate

.

A) 5 B) -5 C) D) 1 Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.

15) Given the function G(t) =

- 7t + 3, evaluate

A) h + 17 B) h - 17 C) h D) h - 12 Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.

39

.

16) Given the function G(t) =

, state the domain in interval notation.

A) [10, ∞) B) (-∞, 10) ∪ (10, ∞) C) (-∞, ∞) D) (-∞, -10) ∪ (10, ∞) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine the domain and range of a function.

17) Given the function f (x) =

, state the domain in interval notation.

A) (-∞, -8] ∪ [8, ∞) B) (-∞, -8) ∪ (8, ∞) C) [-8, 8] D) (-∞, -64] ∪ [64, ∞) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine the domain and range of a function.

18) Given the function h(t) =

, state the domain in interval notation.

A) (-∞, 8] B) (8, ∞) C) (-∞, ∞) D) (-∞, 8) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine the domain and range of a function.

19) Determine if the equation 11x2 + 18 = 10 is a function of x.

Answer: Not a function Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether an equation represents a function.

20) Given the function G(t) = , state the domain in interval notation.

Answer: [-6, 6] Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine the domain and range of a function.

40

21) A projectile is fired straight up from an initial height of 230 feet, and its height is a function of time, h(t) = -16 + 128t + 230 where h is the height in feet and t is the time in second with t = 0 corresponding to the instant it launches. What is the height 4 seconds after launch?

Answer: 486 feet Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.

22) Use the given graph to evaluate the functions. y = r(x)

a. r(-4) b. r(-3) Answer: a. -36 b. -8 Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.

23) Let f (x) = 2x - 21 and find the values of x that corresponds to f (x) = 0.

A) {3/4, -7/2, 11/4} B) {-3/4, 7/2, 11/4} C) {-3/4, 7/2} D) {21/2, 11/4} Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Find the value of a function.

41

24) Use the vertical line test to determine if the graph below defines a function.

Answer: is not a function Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether a relation is a function.

25) Use the vertical line test to determine if the graph below defines a function.

A) is a function B) is not a function C) don't know Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether a relation is a function.

42

26) Classify the following relationship as a function or not a function.

A) a function B) not a function C) don't know Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 01 Learning Objective: Determine whether a relation is a function.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

College Algebra, 5e (Young) 43

Chapter 3

Functions and Their Graphs

3.2 Graphs of Functions; Piecewise Functions; Increasing & Decreasing Functions; Ave Rate of Change 1) Determine if the function in the graph is even, odd, or neither:

A) neither even nor odd B) odd C) even Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

2) Determine if the function h(x) = 7 + 6 is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

44

3) Determine if the function g(x) = 3 + x is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

4) Determine if the function h(t) = 2 - 9 is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

5) Determine if the function f (x) = - 10 is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

6) Determine if the function f (t) = 4|t| + is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

7) Determine if the function h(x) = 7|x + 10| is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

45

8) Determine if the function h(x) = 7|x| + 17 is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

9) Determine if the function f (x) = is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

10) Determine if the function f (x) = is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

11) Determine if the function h(t) = |6t| is even, odd, or neither even nor odd.

Answer: even Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

12) Determine if the function f (x) = is even, odd, or neither even nor odd.

A) even B) odd C) neither even nor odd Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Classify functions as even, odd, or neither.

46

13) The cost of Internet access in a hotel is $18 for the first 25 minutes and $0.07 per minute for each additional minute. Write a function describing the cost of the service as a function of minutes used online.

Answer: C(x) = Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Graph piecewise-defined functions.

14) State (a) the domain, (b) the range, and (c) the x-intervals where the function is increasing, decreasing, and constant. Find the values of f (0) and f (1).

Answer:

f (0) = not defined, f (1) = 0 Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Determine whether functions are increasing, decreasing, or constant.

15) Find the difference quotient

for the function.

f (x) = -9 + 15x - 11 Answer: -18 + 15 - 9h Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Evaluate the difference quotient for a function.

47

16) Graph the piecewise-defined function. State the domain and range in interval notation.

Determine the intervals where the function is increasing, decreasing, or constant.

A)

B)

48

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Graph piecewise-defined functions.

49

17) Graph the piecewise-defined function. State the domain and range in interval notation.

Determine the intervals where the function is increasing, decreasing, or constant.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Graph piecewise-defined functions.

50

18) Graph the piece-wise defined function.

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Graph piecewise-defined functions.

51

19) Match the graph of the piece-wise function.

A)

B)

C)

52

D)

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Graph piecewise-defined functions.

20) State the domain and range for the given graph of the piece-wise function.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Graph piecewise-defined functions.

53

21) (a) Graph the piece-wise function. (b) State the domain and range in interval notation.

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Graph piecewise-defined functions.

22) Given the graph of the piece-wise function, (a) state the domain and range in interval notation and (b) determine the intervals when the function is increasing, decreasing, or constant.

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Graph piecewise-defined functions.

54

23) (a) Graph the piece-wise function. (b) State the domain and range in interval notation. (c) Determine the intervals when the function is increasing, decreasing, or constant.

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Graph piecewise-defined functions.

24) Find the difference quotient

for the function.

f (x) = 11x + 18 Answer: 11 Diff: 1 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Evaluate the difference quotient for a function.

25) Find the average rate of change for the function f (x) = 2

+7

over the range x = 5 to x = 10.

Answer: 3,750 Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Calculate the average rate of change of a function.

55

26) Find the average rate of change for the function f (x) = over the range x = -2 to x = 1. Round the answer to 3 decimal places if necessary.

Answer: -4.333 Diff: 2 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Calculate the average rate of change of a function.

27) Find the average rate of change for the function f (x) = over the range x = 3 to x = 7. Round the answer to 3 decimal places if necessary.

Answer: 0.424 Diff: 3 Var: 1 Chapter/Section: Ch 03, Sec 02 Learning Objective: Calculate the average rate of change of a function.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

College Algebra, 5e (Young) 56

Chapter 4 4.1

Polynomial and Rational Functions

Quadratic Functions

1) Rewrite the quadratic equation in standard form by completing the square. y= - 8x + 19 A) y = +3 B) y = +3 C) y = + 35 D) y = + 35 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Find the equation of a parabola.

2) Rewrite the quadratic equation in standard form by completing the square. y= + 4x - 20 A) y = + 16 B) y = - 24 C) y = - 16 D) y = - 24 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Find the equation of a parabola.

3) Rewrite the quadratic function in standard form by completing the square. y = - - 14x + 3 A) y = - 46 B) y = + 21 C) y = + 52 D) y = - 46 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Find the equation of a parabola.

57

4) Rewrite the quadratic equation in standard form by completing the square. y= - 1x A) y = - 1/4 B) y = C) y = - 1/4 D) y = + 1/4 Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Find the equation of a parabola.

5) Find the vertex of the parabola associated with the quadratic function. y= + 23 A) (-1, -23) B) (1, -23) C) (-1, 23) D) (1, 23) Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function in standard form.

6) Find the vertex of the parabola associated with the quadratic function. y= + 10 A) (8, -10) B) (-8, -10) C) (8, 10) D) (-8, 10) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function in standard form.

7) Find the vertex of the parabola associated with the quadratic equation. y= -3 A) (-1/2, -3) B) (1/2, -3) C) (-1/2, 3) D) (1/2, 3) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function in standard form.

58

8) Find the vertex of the parabola associated with the quadratic function. y = -5 +8 A) (14, -8) B) (14, 8) C) (-14, 8) D) (-5, 8) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function in standard form.

9) Find the vertex of the parabola associated with the quadratic function. y= + 6x + 22 A) (3, -13) B) (-3, -13) C) (-3, 13) D) (3, 13) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function given in general form.

10) Find the vertex of the parabola associated with the quadratic function. y = - + 4x + 6 A) (-2, 34) B) (2, 10) C) (2, 34) D) (-2, 10) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function given in general form.

59

11) Find the standard form of the equation of a parabola whose vertex is (2, 9) and passes through the point (7, -116).

A) y = -5 +9 B) y = -

-9

C) y = -

+9

D) y = -

-9

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function in standard form.

12) Find the general form of the equation of a parabola whose vertex is (2, 1.5) and passes through the point (1, 0.3).

A) y = -1.2 + 4.8x - 3.3 B) y = -1.2 + 4.8x + 3.3 C) y = 1.2 + 4.8x - 3.3 D) y = 1.2 + 4.8x + 3.3 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function given in general form.

13) A rancher has 3000 linear feet of fencing and wants to enclose a rectangular field and then divide it into two equal pastures with an internal fence parallel to one of the rectangular sides.

What is the maximum area of each pasture?

A) 187,500 square feet B) 15,000 square feet C) 375,000 square feet D) 360,000 square feet Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Find the equation of a parabola.

14) Rewrite the quadratic function in standard form by completing the square. y = 4 - 48x + 130 Answer: y = 4 - 14 Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Find the equation of a parabola.

60

15) Find the vertex of the parabola associated with the quadratic function. y = -4 + 76x - 370.5 Answer: (9.5, -9.5) Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function given in general form.

16) A rancher has 1,800 linear feet of fencing and wants to enclose a rectangular field and then divide it into two equal pastures with an internal fence parallel to one of the rectangular sides.

What is the maximum area of each pasture?

Answer: 67,500 square feet Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function given in general form.

17) Find the standard form of the equation of a parabola whose vertex is (5, 10) and passes through the point (3, 30).

Answer: y = 5 + 10 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function in standard form.

18) Find the standard form of the equation of a parabola whose vertex is (8, 4.1) and passes through the point (-2.5, 158.45).

Answer: y = 1.4 - 22.4x + 93.7 Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function in standard form.

19) Graph the quadratic function given in standard form.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function in standard form.

61

20) Graph the quadratic function given in standard form.

A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function in standard form.

62

21) Graph the quadratic function.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function given in general form.

63

22) Graph the quadratic function.

A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function given in general form.

64

23) Match the quadratic function to an equation in standard form.

A) B) C) D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Find the equation of a parabola.

24) Rewrite the quadratic function in standard form by completing the square.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Find the equation of a parabola.

25) A person standing near the edge of a cliff 150 feet above a lake throws a rock upward with an initial speed of 40 feet per second. The height of the rock above the lake at the bottom of the cliff is a function of time and is described by h(t) = -16 + 40t + 150 a. How many seconds will it take until the rock reaches its maximum height?

What is that height? b. At what time will the rock hit the water? Round to two decimal places.

Answer: Part A: 1.25 seconds 175 feet Part B: 4.56 seconds Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Find the equation of a parabola.

65

26) The concentration of a drug in the bloodstream, measured in parts per million, can be modeled with a quadratic function. In 67 minutes the concentration is 49.266 parts per million. The maximum concentration of the drug in the bloodstream occurs in 300 minutes and is 375 parts per million. a. Find a quadratic function that models the concentration of the drug as a function of time in minutes. b. In how many minutes will the drug be eliminated from the bloodstream?

Answer: Part A: C(t) = -0.006 + 375 Part B: 550 minutes Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Find the equation of a parabola.

66

27) Graph the quadratic function. y=

-1

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function in standard form.

67

28) Graph the quadratic function. y= + 2x + 4

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 01 Learning Objective: Graph a quadratic function given in general form.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

College Algebra, 5e (Young) 68

Chapter 4 4.2

Polynomial and Rational Functions

Polynomial Functions of Higher Degree

1) Determine if the function f (x) = 21 + 30 - 30 + 49 is a polynomial. If it is, state the degree.

A) Not a polynomial B) a polynomial of degree 21 C) a polynomial of degree 42 D) a polynomial of degree 4 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify a polynomial function and determine its degree.

2) Determine if the function f (x) =

+ 38

- 25 is a polynomial. If it is, state the degree.

A) Not a polynomial B) a polynomial of degree 17 C) a polynomial of degree 39 D) a polynomial of degree -39 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify a polynomial function and determine its degree.

3) Determine if the function f (x) = 7 (x + 31) is a polynomial. If it is, state the degree.

A) Not a polynomial B) a polynomial of degree 18 C) a polynomial of degree 7 D) a polynomial of degree 25 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify a polynomial function and determine its degree.

69

4) Find all the real zeros (and state their multiplicity) of the polynomial function. y = 2 (x + 7)(x - 1) A) 0, -7, 1 B) -7, 1 C) 0 (multiplicity 4), -7, and 1 D) 0 (multiplicity 4), 7, and -1 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

5) Find all the real zeros (and state their multiplicity) of the polynomial function. y=x A) 0, 1 (multiplicity 2) B) 0, -1, (multiplicity 2) C) 1, 1, (multiplicity 2), 20 (multiplicity 2) D) 0, 1 (multiplicity 2), Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

6) Find all the real zeros (and state their multiplicity) of the polynomial function. y= - 16 + 64 A) 0, 8 B) 0 (multiplicity 4), 8 (multiplicity 2) C) 8 (multiplicity 2) D) 0 (multiplicity 6), 8 (multiplicity 2) Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

7) Find a polynomial of minimum degree with zeros 4, -3 and 5 (of multiplicity 2).

A) y = + 11 + 23 - 95x - 300 B) y = - 6 - 7x + 60 C) y = + 13 - 25x -300 D) y = - 11 + 23 + 95x - 300 Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

70

8) Find a polynomial of minimum degree that has zeros -9, 0 (multiplicity 2) and 7.

A) y = + 2 - 63 B) y = - 2x - 63 C) y = - 2 - 63 D) y = + 2x - 63x Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

9) Find a polynomial of minimum degree with zeros 0, 10 +

, and 10 -

.

A) y = - 20x + 90 B) y = + 20 + 90x C) y = - 20 + 90x D) y = + 20x + 90 Answer: C Diff: 4 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

10) Find a polynomial of minimum degree that has the zeros (with multiplicity 2) and (with multiplicity 2).

A) f (x) = + 10 + 25 B) f (x) = - 10 + 25 C) f (x) = + 25 D) f (x) = + 10x + 25 Answer: B Diff: 4 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

11) For the polynomial function y = (x - 12) (x - 14), determine whether the graph touches or crosses at the x - intercept (-16, 0).

A) crosses the y - axis at (-16, 0) B) touches the y - axis at (-16, 0) C) crosses the x - axis at (-16, 0) D) touches the x - axis at (-16, 0) Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

71

12) For the polynomial function f (x) = (x - 14), determine whether the graph touches or crosses at the x-intercept (0, 0).

A) touches the x-axis at (0, 0) B) crosses the x-axis at (0, 0) C) touches the x-axis at (14, 0) D) neither Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

13) For the polynomial function f (x) = x (x - 1), find the y-intercept.

A) (1, 0) B) (-1, 0) C) (0, 0) D) (0, 1) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

14) For the polynomial function f (x) = (x - 6)(x + 4) , find the y-intercept.

A) (0, -48) B) (0, -96) C) (0, 48) D) (0, 2) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

15) Determine if the function f (x) = 7 (x - 7) is a polynomial. If it is, state the degree.

Answer: polynomial of degree 14 Diff: 1 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify a polynomial function and determine its degree.

72

16) Find all the real zeros (and state their multiplicity) of the polynomial function. ](x - 20) f (x) = Answer: 0 (multiplicity 3), 5 (multiplicity 10), -16 (multiplicity 2), 20 (multiplicity 1) Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

17) Find a polynomial of minimum degree that has the zeros (with multiplicity 2) and (with multiplicity 2).

Answer: y = -4 +4 Diff: 4 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Identify real zeros of a polynomial function and their multiplicities.

18) Sketch the graph of the polynomial function.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

19) Sketch the graph of the polynomial function.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

73

20) Match the polynomial function with its graph.

A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

74

21) Match the polynomial function with its graph.

A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

75

22) Match the graph to the polynomial function.

A) B) C) D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

23) For the polynomial function, (a) list each real zero and its multiplicity; (b) determine whether the graph touches or crosses at each x-intercept; (c) find the y-intercept; (d) determine the end behavior; and (e) sketch the graph.

Answer:

(e)

Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions using transformations.

76

24) For the polynomial function, (a) list each real zero and its multiplicity; (b) determine whether the graph touches or crosses at each x-intercept; (c) find the y-intercept; (d) determine the end behavior; and (e) sketch the graph.

Answer:

(e)

Diff: 2 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions using transformations.

77

25) For the given graph: (a) list each real zero and its smallest possible multiplicity; (b) determine whether the degree of the polynomial is even or odd; (c) determine whether the leading coefficient of the polynomial is positive or negative; (d) find the y-intercept; (e) write an equation for the polynomial function (assume the least degree possible).

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions: x-intercepts; multiplicity (touch/cross) of each zero; end behavior.

78

26) Graph the function by transforming a power function y = xn. f (x) = 2 + 3 Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 04, Sec 02 Learning Objective: Graph polynomial functions using transformations.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

79

College Algebra, 5e (Young) Chapter 5 Exponential and Logarithmic Functions 5.1

Exponential Functions and Their Graphs

1) Approximate the number . Round your answer to two decimal places.

A) 1.59 B) 11,585.24 C) 64.00 D) 1.26 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

2) Approximate the number . Round your answer to two decimal places.

A) 0.58 B) 1.73 C) -1.73 D) -0.58 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

3) Approximate the number . Round your answer to two decimal places.

A) 9.42 B) 1.05 C) 31.54 D) 0.95 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

4) Approximate the number . Round your answer to two decimal places.

A) 31.54 B) 9.42 C) 5.32 D) 7.01 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

80

5) Approximate the number . Round your answer to two decimal places.

A) 22.27 B) 10.39 C) 216.00 D) 4.24 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

6) Given f (x) = , evaluate f (1.8). Round your answer to two decimal places.

A) 2.40 B) 2.30 C) 27.86 D) 0.60 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

7) Given f (x) =

, evaluate f (-0.1). Round your answer to two decimal places.

A) -0.20 B) 0.57 C) 0.87 D) 2.30 Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

8) Find the y-intercept for the exponential function f (x) = + 4.

A) (0, 3) B) (0, -3) C) (0, 4) D) (0, 5) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.; Graph exponential functions.

81

9) Find the y-intercept for the exponential function f (x) = - 8.

A) (0, 12) B) (0, -8) C) (0, -4) D) (0, -7) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.; Graph exponential functions.

10) Find the y-intercept for the exponential function f (x) = + 6.

A) (0, 5) B) (0, -1) C) (0, 7) D) (0, 13) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.; Graph exponential functions.

11) If Gabriel deposits $18,500 in a savings account that earns 3.1% interest per year compounded quarterly, how much money can he expect to be in the account in 2 years? Round your answer to two decimal places.

A) $19,647.00 B) $1,822,882.13 C) $19,678.60 D) $17,383.63 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Solve compound interest problems.

12) If Ashley deposits $10,500 into a savings account that earns 2.7% interest per year compounded monthly, how much money can she expect to be in the account in 3 years? Round your answer to two decimal places.

A) $11,384.86 B) $11,350.50 C) $9682.15 D) $884.86 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Solve compound interest problems.

82

13) If Vu deposits $13,500 in a savings account that earns 1.5% interest per year compounded quarterly, how much money can she expect to be in the account in 3 years? Round your answer to two decimal places.

A) $14,107.50 B) $620.19 C) $12,904.87 D) $14,120.19 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Solve compound interest problems.

14) Evaluate exactly (without using a calculator). For rational exponents, consider converting to radical form first.

Answer: 3 Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

15) Given f (x) = , find f (3.81). Round your answer to two decimal places.

Answer: 8,476.40 Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

16) If Alicia deposits $1,250 in a savings account that earns 5.4% interest per year compounded annually, how much money can she expect to be in the account in 3 years? Round your answer to two decimal places.

Answer: $1,463.63 Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Solve compound interest problems.

83

17) Graph the exponential function. f (x) = Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

18) Use transformation to find the y-intercept and horizontal asymptote and to graph the exponential function. f (x) = -1 Answer: y-intercept: (0, -2) horizontal asymptote is y = -1

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

84

19) Graph the exponential function. f (x) = A)

B)

C)

D)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

85

20) Match the graph to the exponential function.

A) f (x) = -

+1

B) f (x) = +1 C) f (x) = +1 D) f (x) = -1 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

21) A radioactive isotope of selenium, Se, used in the creation of medical images of the pancreas, has a half-life of 119.77 days. If 150 milligrams are given to a patient, how many milligrams are left after 10 days?

Answer: 142 milligrams Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

22) If you put $34,100 in a savings account that pays 3.8% a year compounded continuously, how much will you have in the account in 11 years?

A) $22,450.15 B) $51,794.07 C) $51,795.19 D) $389,628.09 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Solve compound interest problems.

86

23) Approximate the number . Round your answer to two decimal places.

A) 0.12 B) -5.71 C) -0.12 D) 8.17 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Utilize the natural base e.

24) Approximate the number . Round your answer to two decimal places.

A) 4.48 B) 4.71 C) 5.65 D) 10.04 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Utilize the natural base e.

25) Approximate the number . Round your answer to two decimal places.

A) 2.49 B) 1.01 C) 1.56 D) 1.45 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Utilize the natural base e.

26) Approximate the number . Round your answer to two decimal places.

A) 21.20 B) 2.04 C) 1.94 D) 4.06 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Utilize the natural base e.

87

27) For the exponential function f (x) = 1 + , state the y-intercept. Round your answer to two decimal places.

A) (0, 21.09) B) (0, 2) C) (0, 1.05) D) (0, -2) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

28) For the exponential function f (x) = 1 , state the y-intercept. Round your answer to two decimal places.

A) (0, -1.72) B) (0, 0) C) (-1.72, 0) D) (0, 0.63) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

29) For the exponential function f (x) = 1 , state the y-intercept. Round your answer to two decimal places.

A) (0, -1.72) B) (0, 25.46) C) (-1.72, 0) D) (0, 0) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

30) For the exponential function f (x) = 6 - , state the y-intercept. Round your answer to two decimal places.

A) (0, 3.28) B) (0, 5) C) (0, 8.72) D) (3.28, 0) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

88

31) If Juan deposits $4200 in a savings account that earns 2.3% compounded continuously, how much money should he expect to be in the account in 3 years? Round your answer to two decimal places.

A) $300.03 B) $4500.03 C) $4489.80 D) $12,889.80 Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Solve compound interest problems.

32) If Diane deposits $16,713 in a savings account that earns 3.5% interest per year compounded continuously, how much money should she expect to be in the account after 13 years?

A) $24,317.42 B) $316,126.40 C) $26,342.59 D) $9629.59 Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Solve compound interest problems.

33) Approximate the number . Round your answer to two decimal places.

Answer: 0.43 Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Utilize the natural base e.

34) If Vanessa deposits $4,500 in a savings account that earns 3.25% interest per year compounded continuously, how much money should she expect to be in the account in 10 years?

Answer: $6,228.14 Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Solve compound interest problems.

89

35) State the y-intercept and horizontal asymptote, then graph the exponential function. Round the answer for the y-intercept to three decimal places. f (x) = Answer: y-intercept: (0, 1) horizontal asymptote: y = 0

Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

36) Graph the exponential function. f (x) = +1 Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

90

37) Match the graph with the function. f (x) = A)

B)

C)

D)

Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

91

38) Match the graph to the exponential function.

A) f (x) = B) f (x) = C) f (x) = D) f (x) = Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Graph exponential functions.

39) Evaluate exactly (without using a calculator). For rational exponents, consider converting to radical form first.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

40) Evaluate exactly (without using a calculator). For rational exponents, consider converting to radical form first.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

92

41) Evaluate exactly (without using a calculator). For rational exponents, consider converting to radical form first.

Answer: 1 Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Evaluate exponential functions.

42) State the domain and range for the function. Express in interval notation. f (x) = +7 Answer: Domain: (-∞, ∞) Range: (7, ∞) Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Find the domain and range of exponential functions.

43) State the domain and range for the function. Express in interval notation. f (x) = -4 Answer: Domain: (-∞, ∞) Range: (-∞, -4) Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Find the domain and range of exponential functions.

44) State the domain and range for the function. Express in interval notation. f (x) = -9 Answer: Domain: (-∞, ∞) Range: (-9, ∞) Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Find the domain and range of exponential functions.

93

45) State the domain and range for the function. Express in interval notation. f (x) = -9 Answer: Domain: (-∞, ∞) Range: (-∞, -9) Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 01 Learning Objective: Find the domain and range of exponential functions.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

94

College Algebra, 5e (Young) Chapter 5 Exponential and Logarithmic Functions 5.2

Logarithmic Functions and Their Graphs

1) Write the logarithmic equation in its equivalent exponential form.

25 = -2 A) B) C)

= 1/5 = 25 = 25

D) = 25 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Convert logarithmic expressions to exponential expressions.

2) Write the logarithmic equation in its equivalent exponential form.

32 = 5 A) B)

=2 = 32

C) = 32 D) =2 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Convert logarithmic expressions to exponential expressions.

3) Write the logarithmic equation in its equivalent exponential form. log 1000 = 3 A) = 1000 B) = 1000 C) = 1000 D) = 10 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Convert logarithmic expressions to exponential expressions.

95

4) Write the logarithmic equation in its equivalent exponential form. log 0.01 = -2 A) = 0.01 B) = 0.01 C) = 0.01 D) = 10 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Convert logarithmic expressions to exponential expressions.

5) Write the exponential equation in its equivalent logarithmic form.

5= A) ln 125 = 5 B)

= 125

C)

125 = 5

D)

5=

Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Convert exponential expressions to logarithmic expressions.

6) Write the exponential equation in its equivalent logarithmic form. = 625 A) ln 625 = 4 B) 625 = 4 C)

4=5

D) log 625 = 4 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Convert exponential expressions to logarithmic expressions.

96

7) Write the exponential equation in its equivalent logarithmic form. = A)

=4

B)

=4

C) log

=4

D)

=4

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Convert exponential expressions to logarithmic expressions.

8) Evaluate the logarithm exactly.

1 A) 1 B) 37 C) 0 D) undefined Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Evaluate logarithmic expressions exactly by inspection.

9) Approximate the common logarithm using the calculator. Round your answer to two decimal places. log 838 A) 2.92 B) 8380 C) 6.73 D) 2277.92 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Approximate common and natural logarithms using a calculator.

97

10) Approximate the common logarithm using the calculator. Round your answer to two decimal places. log 0.0101 A) -4.60 B) -2.00 C) 0.03 D) 0.101 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Approximate common and natural logarithms using a calculator.

11) Approximate the natural logarithm using a calculator. Round your answer to two decimal places. ln 33 A) 1.52 B) 89.70 C) 3.50 D) 330 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Approximate common and natural logarithms using a calculator.

12) Approximate the natural logarithm using a calculator. Round your answer to two decimal places. ln 0.0084 A) -2.08 B) 0.08 C) 0.02 D) -4.78 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Approximate common and natural logarithms using a calculator.

13) State the domain of the logarithm function f (x) =

(10 - x) in interval notation.

A) (10, ∞) B) (-∞, 10) C) (-∞, 10] D) (0, ∞) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Determine domain restrictions on logarithmic functions.

98

14) State the domain of the logarithm function f (x) =

.

A) (-∞, ∞) B) (-3, 3) C) (0, ∞) D) (-∞, -3) ∪ (-3, ∞) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Determine domain restrictions on logarithmic functions.

15) State the domain of the logarithm function f (x) =

.

A) (0, ∞) B) [- 4, 4] C) (- 4, 4) D) (-∞, 4) ∪ ( 4, ∞) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Determine domain restrictions on logarithmic functions.

16) Write the logarithmic equation in its equivalent exponential form.

21.11 = 2.2 Answer: = 21.11 Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Convert logarithmic expressions to exponential expressions.

17) State the domain of the logarithmic function f (x) =

(47 - x) in interval notation.

Answer: (-∞, 47) Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Determine domain restrictions on logarithmic functions.

18) Write the exponential equation in its equivalent logarithmic form. = 3.48 Answer: 1.8 = 2 Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Convert exponential expressions to logarithmic expressions.

99

19) Graph the logarithmic function. f (x) = (3 - x) Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Graph logarithmic functions.

20) Graph the logarithmic function using transformation techniques. f (x) = (2 - x) Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Graph logarithmic functions.

100

21) Match the graph with the logarithmic function. f(x) = (3 - x) A)

B)

C)

D)

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Graph logarithmic functions.

101

22) Match the graph to the logarithmic function.

A)

f (x) =

(x + 1) - 1

B)

f (x) =

(x - 1) - 1

C)

f (x) =

(x - 1) + 1

D)

f (x) =

(x + 1) + 1

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Graph logarithmic functions.

23) A city experienced a major earthquake. The energy released measured Calculate the magnitude of the earthquake using the Richter scale.

A) 11.3 B) 7.5 C) 17.4 D) 13.4 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Evaluate logarithmic expressions exactly by inspection.

24) A substance has an approximate hydrogen ion concentration of about 3.89 × Calculate its pH value.

A) 12.1 B) 25.1 C) -12.1 D) 10.9 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Evaluate logarithmic expressions exactly by inspection.

102

.

25) Evaluate the logarithm exactly.

161,051 A) 1 B) 11 C) 5 D) undefined Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Evaluate logarithmic expressions exactly by inspection.

26) Evaluate the logarithm exactly.

- 243 A) 1 B) 3 C) 5 D) undefined Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Evaluate logarithmic expressions exactly by inspection.

103

27) Graph the logarithmic function. f (x) = +1

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Graph logarithmic functions.

104

28) Graph the logarithmic function. f (x) = (x + 5)

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Graph logarithmic functions.

105

29) Graph the logarithmic function. f (x) = -3 x

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Graph logarithmic functions.

106

30) Graph the logarithmic function on a logarithmic scale. f (x) = -3 x

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 02 Learning Objective: Graph functions using a logarithmic scale.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

107

College Algebra, 5e (Young) Chapter 5 Exponential and Logarithmic Functions 5.3

Properties of Logarithms

1) Use the properties of logarithms to simplify the expression.

63 A) 63 B) 1 C) 0 D) not defined Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

2) Use the properties of logarithms to simplify the expression.

A) -2 ln 4 B) 16 C) 1/16 D) -8 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

3) Use the properties of logarithms to simplify the expression.

A) 256 B) 16 C) 1/256 D) 81 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

108

4) Use the properties of logarithms to simplify the expression.

125 A) 5 B) 125 C) 3 D) 1/3 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

5) Use the properties of logarithms to simplify the expression.

A) 2 B) 1/2 C) 1 D) 0 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

6) Write the expression as a sum or difference of logarithms.

A) 5

x+8

y

B) 5

x-8

y

C) -8

x-5

y

D) -40

(xy)

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Write a single logarithm as a sum or difference of logarithms.

109

7) Write the expression as a sum or difference of logarithms.

A) 5

x+

y-5

z

B) 5

x+

y+5

z

C) 5

x-

y - 5logbz

D)

logb(xyz)

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Write a single logarithm as a sum or difference of logarithms.

8) Write the expression as a sum or difference of logarithms.

A)

(xy)

B) 6

(xz)

C)

x+

z

D)

x-

z

Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Write a single logarithm as a sum or difference of logarithms.

110

9) Write the expression as a sum or difference of logarithms.

A) 4

x+

x+

6-

B) 4

x+

(x + 6) +

(x + 9)

C) 4

x+

(x + 6) -

(x + 9)

D) 4

x+

x+

6-

(x + 9)

x-

9

Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Write a single logarithm as a sum or difference of logarithms.

10) Write the expression as a single logarithm.

5log u + 6log v A) log B) log C) log (uv) D) log Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Write a logarithmic expression as a single logarithm.

111

11) Write the expression as a single logarithm.

5log u - log v - 9log z A) log B) log

C) log

D) log Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Write a logarithmic expression as a single logarithm.

12) Write the expression as a single logarithm. ln x -

ln y

A) ln

B) ln

C) ln

D) Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Write a logarithmic expression as a single logarithm.

112

13) Evaluate the logarithm using the change-of-base formula. Round your answer to two decimal places.

13 A) 3.52 B) 1.53 C) 2.68 D) 0.37 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

14) Evaluate the logarithm using the change-of-base formula. Round your answer to two decimal places.

26 A) 1.67 B) 0.60 C) 5.20 D) 2.26 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

15) Use the properties of logarithms to simplify the expression.

Answer: 2 Diff: 3 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

16) Write the expression as a single logarithm. ln(x + 9) - 5ln(x - 4) Answer: ln Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Write a logarithmic expression as a single logarithm.

113

17) Evaluate the logarithm using the change of base formula. Round your answer to two decimal places.

8.1 Answer: 3.26 Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

18) If a seismologist records the energy of P waves as 4.1 × joules and the energy of S waves as what is the total energy? What would the combined effect be on the Richter scale?

A) Total energy is 4.2 × joules and 4.8 on the Richter scale.

B) Total energy is 1.3 × joules and 11.1 on the Richter scale.

C) Total energy is 4.3 × joules and -1.2 on the Richter scale.

D) Total energy is 3.4 × joules and 11.4 on the Richter scale.

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Write a logarithmic expression as a single logarithm.

19) Use the properties of logarithms to simplify the expression.

A) 3 B) 1/3 C) 1 D) 0 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

114

20) Evaluate the logarithm using the change of base formula. Round your answer to two decimal places.

41 Answer: 3.38 Diff: 2 Var: 1 Chapter/Section: Ch 05, Sec 03 Learning Objective: Evaluate logarithms of a general base (other than base 10 or e).

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

115

College Algebra, 5e (Young) Chapter 7 Matrices 7.1

Matrices and Systems of Linear Equations

1) Write the system of linear equations as an augmented matrix.

6x + 4y = -9 8x + 3y = 10 A) B) C) D) Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

2) Write the system of linear equations as an augmented matrix.

10x - 12y = 26 29x + 22y = -7 A) B) C) D) Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

116

3) Write the system of linear equations as an augmented matrix.

7x - 14y + 28z = -18 -28x + 26y - 23z = 13 -15x - 12y - 17z = -1 A)

B)

C)

D) Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

4) Write the system of linear equations as an augmented matrix.

18x - 28y + 12z = -25 -17x + 29y + 16z = 11 27x - 25y - 23z = 14 A)

B)

C)

D) Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

117

5) Write the system of linear equations represented by the augmented matrix. Utilize the variables x and y.

A) 14x - 7y = 30 28x + 2y = 16 B) 14x + 7y = 30 28x - 2y = 16 C) 28x + 7y = 30 14x - 2y = 16 D) 14x + 2y = 16 28x - 16y = 30 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

6) Write the system of linear equations as represented by the augmented matrix. Utilize the variables x and y.

A) -6x - 2y = -12 5x + 7y = -20 B) 5x - 2y = -20 -6x + 7y = -12 C) 5x + 7y = -12 -6x + 2y = -20 D) 5x - 2y = -12 -6x + 7y = -20 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

118

7) Write the system of linear equations as represented by the augmented matrix. Utilize the variables x, y, and z.

A) -4x + 7y - 2z = 15 10x - 18y + 19z = -30 20x + 12y + 17z = 9 B) -4x - 7y + 2z = 15 10x + 18y + 19z = -30 20x + 12y + 17z = 9 C) -4x + 7y - 2z = -15 10x - 18y + 19z = -30 20x - 12y - 17z = 9 D) -4x + 7y - 2z = -30 10x - 18y + 19z = 15 20x - 12y + 17z = 9 Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

8) Use row operations to transform the matrix to reduced row-echelon form.

A) B) C) D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Perform row operations on an augmented matrix.; Write a matrix in reduced row-echelon form.; Write a matrix in row-echelon form.

119

9) Use row operations to transform the matrix to reduced row-echelon form.

A)

B)

C)

D) Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Perform row operations on an augmented matrix.; Write a matrix in reduced row-echelon form.; Write a matrix in row-echelon form.

10) Use row operations to transform the matrix to reduced row-echelon form.

A)

B)

C)

D) Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Perform row operations on an augmented matrix.; Write a matrix in reduced row-echelon form.; Write a matrix in row-echelon form.

120

11) Perform the row operation

→

+

on the matrix and write the resulting matrix.

A) B) C) D) Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Perform row operations on an augmented matrix.

12) Perform the row operation -2

+

→

on the matrix and write the resulting matrix.

A) B) C) D) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Perform row operations on an augmented matrix.

121

13) Perform the row operation

→

+

on the matrix and write the resulting matrix.

A)

B)

C)

D) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Perform row operations on an augmented matrix.

14) Perform the row operation -6

+

→

on the matrix and write the resulting matrix.

A)

B)

C)

D) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Perform row operations on an augmented matrix.

122

15) Perform the row operations -5

+

→

and

4

+

→

on the matrix and write

the resulting matrix.

A)

B)

C)

D) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Perform row operations on an augmented matrix.

16) Use row operations to transform the matrix to reduced row-echelon form.

A) B) C) D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a matrix in reduced row-echelon form.

123

17) Use row operations to transform the matrix to reduced row-echelon form.

A)

B)

C)

D) Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a matrix in reduced row-echelon form.

18) Solve the system of linear equations using Gaussian elimination with back-substitution.

-2x - 7y = -27 50x + 6y = 50 A) (5, -4) B) (-4, 5) C) (-2, -20) D) (-20, -2) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Solve systems of linear equations using Gaussian elimination with back-substitution.

124

19) Solve the system of linear equations using Gaussian elimination with back-substitution.

5x + 8y + 8z = 29 2x + 8y + 3z = 31 2x + 4y + 6z = 12 A) (4, -1, 1) B) (-1, 1, 4) C) (1, -1, 4) D) (1, 4, -1) Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Solve systems of linear equations using Gaussian elimination with back-substitution.

20) Write the system of linear equations represented by the augmented matrix. Utilize the variables x, y, and z.

Answer: 5x + 40y - 29z = -23 28x - 33y - 5z = 37 42x + 13y + 42z = 12 Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

21) Write the system of equations as represented by the augmented matrix. Utilize the variables x and y.

Answer: -8x + 22y = -22 15x - 23y = 5 Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

125

22) Perform the row operation 5

+

→

on the matrix and write the resulting matrix.

Answer: Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Perform row operations on an augmented matrix.

23) Use row operations to transform the matrix to reduced form.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Perform row operations on an augmented matrix.; Write a matrix in reduced row-echelon form.

24) Brian and Beatrice decide to place $18,200 of their savings into investments. They put some in a money market account earning 4.5% interest, some in a mutual fund that has been averaging 5.7% a year, and some in a stock that rose 8.1% last year. If they put $4000 more in the money market than in the mutual fund and the mutual fund and stocks have the same growth in the next year as they did in the previous year, they will earn $1036.20 in a year. How much money did they put in each of the three investments?

A) $3100 at 4.5%, $7100 at 5.7%, $8000 at 8.1% B) $8900 at 4.5%, $4900 at 5.7%, $4400 at 8.1% C) $4900 at 4.5%, $4400 at 5.7%, $8900 at 8.1% D) $7100 at 4.5%, $8000 at 5.7%, $3100 at 8.1% Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

126

25) Josh and Ann decide to place $12,200 of their savings into investments. They put some in a money market account earning 2.7% interest, some in a mutual fund that has been averaging 5.9% a year, and some in a stock that rose 9.7% last year. If they put $1,200 more in the money market than in the mutual fund and the mutual fund and stocks have the same growth in the next year as they did in the previous year, they will earn $915.80 in a year. How much money did they put in each of the three investments?

Answer: $2,900 at 2.7%, $1,700 at 5.9%, $7,600 at 9.7% Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

26) Find the values of a, b, and c such that the graph of the quadratic function passes through the points and Answer: a = 4, b = -6, c = -5 Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Write a system of linear equations as an augmented matrix.

27) Write the order of the matrix.

A) 3 × 2 B) 2 × 2 C) 2 × 3 D) 3 × 3 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Determine the order of a matrix.

28) Write the order of the matrix.

A) 3 × 3 B) 2 × 2 C) 2 × 3 D) 3 × 2 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Determine the order of a matrix.

127

29) Solve the system of linear equations for x, y, and z using Gauss-Jordan elimination.

A) (3, -1, -2) B) (3, 1, -2) C) (-2, -1, 3) D) (-2, 1, 3) Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Solve systems of linear equations using Gauss-Jordan elimination.

30) Solve the system of linear equations for x, y, and z using Gauss-Jordan elimination.

A) (-2, 4, -3) B) (-3, 4, 2) C) (2, 4, -3) D) (4, -3, 2) Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Solve systems of linear equations using Gauss-Jordan elimination.

31) Solve the system of linear equations for x, y, and z using Gauss-Jordan elimination.

3x - 7y + 2z = -37 8x - 2y - 6z = 12 -5x + 7y + 2z = 35 Answer: (5, 8, 2) Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Solve systems of linear equations using Gauss-Jordan elimination.

128

32) Solve the system of linear equations using Gaussian elimination with back-substitution.

A) (3, -4, 1) B) (3, 4, 1) C) (1, -4, 3) D) (1, 4, 3) Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Solve systems of linear equations using Gaussian elimination with back-substitution.

33) Write the order of the matrix.

A) 3 × 2 B) 2 × 2 C) 2 × 3 D) 3 × 3 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Determine the order of a matrix.

34) Write the order of the matrix.

A) 3 × 3 B) 2 × 2 C) 2 × 3 D) 3 × 2 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Determine the order of a matrix.

129

35) Write the order of the matrix.

A) 4 × 1 B) 4 × 4 C) 1 × 4 D) 1 × 1 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 01 Learning Objective: Determine the order of a matrix.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

130

College Algebra, 5e (Young) Chapter 7 Matrices 7.2

Matrix Algebra

1) Calculate A + B if A =

and B =

.

A) B) C) D) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Add and subtract matrices.

2) Calculate AB if A =

and B =

.

A) B) C) D) Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Multiply two matrices.

131

3) Calculate 3B - 2A if A =

and B =

.

A) B) C) D) Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Add and subtract matrices.; Perform scalar multiplication.

4) Calculate D(A + B) if A =

,B=

and D =

A) B) C) D) Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Add and subtract matrices.; Multiply two matrices.

5) Calculate AB if A =

and B =

.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Multiply two matrices.

132

.

6) Solve for the indicated variables. = A) x = 5, y = -10, z = -7 B) x = -10, y = 5, z = -7 C) x = -10, y = -5, z = -4 D) x = 10, y = 5, z = -7 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Use equality of matrices.

7) Calculate -4A - 5B if A =

and B =

.

A) B) C) D) Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Add and subtract matrices.; Perform scalar multiplication.

133

8) A company has two rubrics for scoring job applicants based on weighing education, experience, and the interview differently.

Matrix A Rubric 1

Rubric 2

Education Experience Interview Applications receive a score from 1 to 10 in each category (education, experience, and interview).

Two applicants are shown in matrix B: Matrix B Education Experience Interview Applicant1 Applicant2 What is the order of BA? What does each entry in BA tell us?

Answer: The order of BA is 2 by 2.

BA = Each entry tells the rubric scoring of each applicant.

Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Multiply two matrices.

9) Perform the indicated operations for the expression, if possible.

A=

B=

C=

AB - 9C A)

B) C) D) not possible Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Add and subtract matrices.; Multiply two matrices.; Perform scalar multiplication.

134

10) Perform the indicated operations for the expression, if possible.

A=

B= - 3B

A)

B)

C) D) not possible Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Add and subtract matrices.; Multiply two matrices.; Perform scalar multiplication.

11) Write the order of the matrix.

A) 3 × 2 B) 2 × 2 C) 2 × 3 D) 3 × 3 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Determine the order of a matrix.

135

12) Write the order of the matrix.

A) 3 × 3 B) 2 × 2 C) 2 × 3 D) 3 × 2 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Determine the order of a matrix.

13) Write the order of the matrix.

A) 4 × 1 B) 4 × 4 C) 1 × 4 D) 1 × 1 Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Determine the order of a matrix.

14) Solve for the indicated variables. = A) (-6, 3) B) (3, 6) C) (6, 3) D) (-6, -3) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Use equality of matrices.

136

15) Solve for the indicated variables. = A) (-4, 5) B) (-1, 6) C) (2, 8) D) (4, 5) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Use equality of matrices.

16) Solve for the indicated variables. = A) (-5, -4) B) (-4, 5) C) (5, -4) D) (-5, 4) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Use equality of matrices.

17) Calculate AB if A =

and B =

.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Multiply two matrices.

137

18) Calculate

if A =

.

A) B) C) D) Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 07, Sec 02 Learning Objective: Multiply two matrices.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

College Algebra, 5e (Young) 138

Chapter 8 8.1

Conics and Systems of Nonlinear Equations and Inequalities

Conic Basics

1) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

- 2x + + 8y + 4 = 7 Select the choice that best describes the graph of the equation.

A) parabola B) ellipse C) circle D) hyperbola Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

2) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

16 + 4 = 81 A) parabola B) ellipse C) circle D) hyperbola Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

3) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

-y=6 A) parabola B) ellipse C) circle D) hyperbola Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

139

4) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

81 - 49 = 4 A) parabola B) ellipse C) circle D) hyperbola Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

5) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. + 6x + - 10y + 11 = 18 A) parabola B) ellipse C) circle D) hyperbola Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

6) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

15 - 3x + 4 - 16y + 4 = 17 A) parabola B) ellipse C) circle D) hyperbola Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

140

7) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

-1 - 18x - y = 12 A) parabola B) ellipse C) circle D) hyperbola Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

8) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

18 - 14x- 16 + 14y + 8 = -7 Select the choice that best describes the graph of the equation.

A) parabola B) ellipse C) circle D) hyperbola Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

9) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points exactly four units from the point (-14, -17) A) parabola B) ellipse C) circle D) hyperbola Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

10) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points equidistant from the point (8, 2) and the line y = -4.

A) parabola B) ellipse C) circle D) hyperbola Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

141

11) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose distance from the point (3, 14) plus the distance from the point is exactly 7 units.

A) parabola B) ellipse C) circle D) hyperbola Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

12) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose difference of the distances to the points 18 units.

A) parabola B) ellipse C) circle D) hyperbola Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

13) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points exactly 3 units from the point (14, -20).

A) parabola B) ellipse C) circle D) hyperbola Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

14) Identify the conic section as a parabola, circle, ellipse, or hyperbola: The set of all points equidistant from the point (-11, -4) and the line A) parabola B) ellipse C) circle D) hyperbola Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

142

and

is exactly

15) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose distance from the point (-5, 9) plus the distance from the point exactly 8 units.

A) parabola B) ellipse C) circle D) hyperbola Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

is

16) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose difference of the distances to the points (-11, 7) and (4, 7) is exactly 1 units.

A) parabola B) ellipse C) circle D) hyperbola Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

17) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose distance from the point (-2, 15) plus the distance from the point is exactly 16.

A) parabola B) ellipse C) circle D) hyperbola Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

18) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points equidistant from the point (20, -12) and the line A) parabola B) ellipse C) circle D) hyperbola Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

143

19) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

45 - 41 = 30 Answer: hyperbola Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

20) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points equidistant from the point (4, -15) and from the line x = -4.

Answer: parabola Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

21) Identify the conic section as a parabola, ellipse, circle, or hyperbola: The set of all points whose distance from the point (4, 9) plus the distance from the point exactly 39 units.

Answer: ellipse Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Define conics.

22) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

- 4x + + 6y + 4 = 7 Answer: circle Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

23) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

16 + 25 = 81 Answer: ellipse Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

24) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

-y=6 Answer: parabola Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

144

is

25) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

100 - 4 = 49 Answer: hyperbola Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

26) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. + 4x + - 6y + 20 = 3 Answer: circle Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

27) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

3 - 7x + 17 - 7y + 16 = 7 Answer: ellipse Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

28) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

-4 - 18x - y = 15 Answer: parabola Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

145

29) Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola.

17 - 16x - 4 + 13y + 16 = 8 Answer: hyperbola Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 01 Learning Objective: Recognize the algebraic equation associated with each conic.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

146

College Algebra, 5e (Young) Chapter 8 Conics and Systems of Nonlinear Equations and Inequalities 8.2

The Parabola

1) Find an equation for the parabola with vertex (4, 5) and focus (4, 11).

A) = 24( y - 5) B) = 24( y - 4) C) = 6( y - 5) D) = 24( y + 5) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

2) Find an equation for the parabola with vertex (1, 8) and focus (3, 8).

A) = -2(x - 1) B) = -8(x + 1) C) = -8(x - 1) D) = -8( y - 1) Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

3) Find an equation for the parabola with vertex (2, 8) and focus (4, 8).

A) - 16x - 8y + 48 = 0 B) - 16y - 8x + 48 = 0 C) - 16y + 8x + 48 = 0 D) - 16x + 8y + 48 = 0 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

147

4) Find an equation for the parabola with vertex (-2, 10) and focus (-5, 10).

A) - 20y + 12x + 124 = 0 B) - 20x + 12y + 124 = 0 C) - 20x - 12y + 124 = 0 D) - 20y - 12x + 124 = 0 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

5) Find an equation for the parabola with vertex (8, 3) and focus (8, 10).

A) - 16y - 28x + 148 = 0 B) - 16x + 28y + 148 = 0 C) - 16x - 28y + 148 = 0 D) - 16y + 28x + 148 = 0 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

6) Find an equation for the parabola with vertex (7, 1) and focus (7, -5).

A) - 14x + 24y + 25 = 0 B) - 14x - 24y + 25 = 0 C) - 14y - 24x + 25 = 0 D) + 14y + 24x + 25 = 0 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

7) Find an equation for the parabola with focus (14, 3) and directrix x = 4.

A) - 6x + 20y + 189 = 0 B) - 6x - 20y + 189 = 0 C) - 6y - 20x + 189 = 0 D) - 6y + 20x + 189 = 0 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

148

8) Find an equation for the parabola with focus (9, 7) and directrix x = 11.

A) - 14y - 4x + 9 = 0 B) - 14y + 4x + 9 = 0 C) - 14x - 4y + 9 = 0 D) - 14x + 4y + 9 = 0 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

9) Find an equation for the parabola with focus (1, 11) and directrix y = 7.

A) - 2y - 8x + 73 = 0 B) - 2x - 8y + 73 = 0 C) - 2x + 8y + 73 = 0 D) - 2y + 8x + 73 = 0 Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

10) Find an equation for the parabola with focus (8, -2) and directrix y = 4.

A) - 16x + 12y + 52 = 0 B) - 16x - 12y + 52 = 0 C) - 16x + 12y + 52 = 0 D) - 16x - 12y + 52 = 0 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

11) Find an equation of the form A + Bx + Cy + D = 0 or A + By + Cx + D = 0 for the parabola with vertex (-1, 6) and focus (5, 6).

Answer: - 12y - 24x - 12 = 0 Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

12) Find an equation of the form A + Bx + Cy + D = 0 or A + By + Cx + D = 0 for the parabola with focus (10, -8) and directrix y = 8.

Answer: - 20x + 32y + 100 = 0 Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

149

13) Graph the equation.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

14) Write an equation for the parabola.

Answer:

Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

150

15) Match the parabola to the equation.

A) B) C) D) Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

151

16) Match the equation to the parabola.

A)

B)

C)

D)

152

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

17) Graph the parabola and label the coordinates of the vertex.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

18) Graph the parabola and label the coordinates of the vertex.

Answer:

Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

153

19) Match the parabola to an equation in standard form.

A) B) C) D) Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

20) Match the parabola to an equation in general form.

A) B) C) D) Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

154

21) Match the equation to the parabola.

A)

B)

C)

D)

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

155

22) Match the equation to the parabola.

A)

B)

C)

D)

Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

156

23) Write an equation for the parabola in standard form.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

24) Write an equation for the parabola in standard form.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

157

25) Write an equation for the parabola in general form.

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

26) A satellite dish measures 72 feet across its opening and 9 feet deep at its center. The receiver should be placed at the focus of the parabolic dish. Where is the focus?

A) The focus will be at (0, 9) so the receiver should be placed 36 feet from the vertex.

B) The focus will be at (0, 36) so the receiver should be placed 9 feet from the vertex.

C) The focus will be at (36, 0) so the receiver should be placed 9 feet from the vertex.

D) The focus will be at (0, 36) so the receiver should be placed 72 feet from the vertex.

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the origin.

27) A bridge with a parabolic shape has an opening 98 feet wide at the base of the bridge (where the bridge meets the water), and the height in the center of the bridge is 40 feet. A sailboat whose mast reaches 50 feet above the water is traveling under the bridge 23 feet from the center of the bridge. Will it clear the bridge without scraping its mast? Justify your answer.

A) No. The opening height is 50 feet, and the mast is 31.2 feet.

B) Yes. The opening height is 50 feet, and the mast is 31.2 feet.

C) No. The opening height is 31.2 feet, and the mast is 50 feet.

D) No. The opening height is 32 feet, and the mast is 50 feet.

Answer: C Diff: 3 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the origin.

28) Find the vertex of the parabola with equation = 20( y - 9).

Answer: (8, 9) Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

158

29) Find the vertex of the parabola with equation = -24(x - 4).

Answer: (4, 1) Diff: 1 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

30) Find the vertex of the parabola with equation - 14y - 24x + 25 = 0.

Answer: (1, 7) Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

31) Find the vertex of the parabola with equation - 2y + 8x + 41 = 0.

Answer: (-5, 1) Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Find the equation of a parabola whose vertex is at the point (h, k).

32) Find the focus of the parabola with equation = 24( y - 8).

Answer: (3, 14) Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

33) Find the focus of the parabola with equation = -12(x - 2).

Answer: (5, 4) Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

34) Find the focus of the parabola with equation - 16y - 4x + 4 = 0.

Answer: (16, 8) Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

35) Find the focus of the parabola with equation - 14y + 32x + 209 = 0.

Answer: (-13, 7) Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

159

36) Find the equation of the directrix of the parabola with equation = 12( y - 5).

Answer: x = 2 Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

37) Find the equation of the directrix of the parabola with equation = -8(x - 3).

Answer: y = 1 Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

38) Find the equation of the directrix of the parabola with equation - 12y - 12x + 12 = 0.

Answer: y = -1 Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

39) Find the equation of the directrix of the parabola with equation - 6x - 32y + 201 = 0.

Answer: x = -2 Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

40) Find the length of the latus rectum of the parabola with equation = 20( y - 4).

Answer: 20 Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

41) Find the length of the latus rectum of the parabola with equation = -8(x - 7).

Answer: 8 Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

42) Find the length of the latus rectum of the parabola with equation - 18y - 4x + 77 = 0.

Answer: 4 Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

160

43) Find the length of the latus rectum of the parabola with equation - 16x - 8y + 120 = 0.

Answer: 8 Diff: 2 Var: 1 Chapter/Section: Ch 08, Sec 02 Learning Objective: Graph a parabola given the focus, directrix, and vertex.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

161

College Algebra, 5e (Young) Chapter 9 Sequences, Series, and Probability 9.1

Sequences and Series

1) Write the first four terms of the following sequence. Assume that n starts at 1. = A)

= 1,

=

B)

= 7,

=

,

=

,

=

C)

= 1,

=

,

=

,

=

D)

=

,

,

=

=

,

,

=

=

,

=

Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Find terms of a sequence given the general term.

2) Write the first four terms of the following sequence. Assume that n starts at 1. = A)

= 1,

=

B)

=

,

=

,

=

,

=

C)

=

,

=

,

=

,

=

D)

= 1,

=

,

,

=

=

,

,

=

=

Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Find terms of a sequence given the general term.

162

3) Write the first four terms of the following sequence. Assume that n starts at 1. = A)

= 1,

= -22,

B)

= -11,

= -11,

C)

= -22,

=-

D)

= 1,

= -22,

= -11,

= -11

= -11, ,

==-

= -11 ,

,

==-

Answer: C Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Find terms of a sequence given the general term.

4) Find the term A)

=

B)

= 243

C)

= 15

D)

=

of the sequence

=

.

Answer: A Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Find terms of a sequence given the general term.

5) Find the term A)

=

B)

=6

C)

= 19

D)

=

of the sequence

=

.

Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Find terms of a sequence given the general term.

163

6) Find the term A)

=9

B)

=9

C)

= 1/ 9

D)

= 1/9

of the sequence

=

.

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Find terms of a sequence given the general term.

7) Find the term A)

=-

B)

= -51

C)

=-

D)

= 10

of the sequence

=

.

Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Find terms of a sequence given the general term.

8) Write an expression for the term of the sequence 1, 6, 11, 16, 21, ...

A) = 5n - 4, for n = 1, 2, 3, ...

B)

= 4n + 5, for n = 1, 2, 3, ...

C)

= 4n - 5, for n = 1, 2, 3, ...

D)

= n + 4, for n = 1, 2, 3, ...

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Look for a pattern in a sequence and find the general term.

164

9) Write an expression for the A)

=

, for n = 1, 2, 3, ...

B)

=

, for n = 1, 2, 3, ...

C)

= n + 2, for n = 1, 2, 3, ...

D)

= 3n + 2, for n = 1, 2, 3, ...

term of the sequence

,

,

,

,

, ...

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Look for a pattern in a sequence and find the general term.

10) Simplify the ratio of factorials

.

A) 10 B) 2 C) 24 D) 30 Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Apply factorial notation.

11) Simplify the ratio of factorials

.

A) 1190 B) 2 C) 68 D) 1155 Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Apply factorial notation.

165

12) Simplify the ratio of factorials

.

A) 188 B) 4 C) 79,727,040 D) 8832 Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Apply factorial notation.

13) Write the first four terms of the sequence defined by the recursion formula. Assume the sequence begins at 1.

A)

= 1,

= 2,

= 12,

= 22

B)

= 2,

= 12,

= 22,

= 32

C)

= 0,

= 2,

= 12,

= 22

D)

= 12,

= 22,

= 32,

= 42

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Apply recursion formulas.

14) Write the first four terms of the sequence defined by the recursion formula. Assume the sequence begins at 1.

A)

= 2,

= 3,

= 12,

= 18

B)

= 1,

= 2,

= 3,

= 36

C)

= 36,

= 648,

D)

= 2,

= 3,

= 139,968, = 36,

= 544,195,584

= 648

Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Apply recursion formulas.

166

15) Evaluate the finite series.

A) 26 B) 15 C) 14 D) 18 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Use summation (sigma) notation to represent a series.

16) Evaluate the finite series.

A) 40 B) 120 C) 118 D) 324 Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Use summation (sigma) notation to represent a series.

17) Evaluate the finite series.

A) 15,625 B) 3413 C) 55 D) 701 Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Use summation (sigma) notation to represent a series.

18) Write the first four terms of the sequence. Assume that n starts at 1. = Answer:

= 256,

= -16,384,

= 331,776,

= -4,194,304

Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Find terms of a sequence given the general term.

167

19) Find the term Answer:

of the sequence

=

.

=

Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Find terms of a sequence given the general term.

20) Simplify the ratio of factorials.

Answer: 22,650 Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Apply factorial notation.

21) Evaluate the finite series.

Answer: 16 Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Evaluate a series.

22) Dylan sells his car freshman year and puts $3100 in an account that earns 6.2% interest compounded monthly. The balance in the account after n months is = 3100 Calculate

n = 1, 2, 3,... .

What does

represent?

A) $3132.12,

represents the balance in 24 months or 2 years.

B) $3508.13,

represents the balance in 24 years.

C) $3508.13,

represents the balance in 24 months or 2 years.

D) $74,784.40,

represents the balance in 24 months or 2 years.

Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Find terms of a sequence given the general term.

168

23) Simplify the ratio of factorials

.

Answer: 25 + 145n + 210 Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Apply factorial notation.

24) Write the first four terms of the sequence defined by the recursion formula. Assume the sequence begins at 1.

Answer:

= 2,

= 24,

= 96,

= 96

Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Apply recursion formulas.

25) Evaluate the finite series.

Answer: 27 +81 + 243 + 729 Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Evaluate a series.

26) Evaluate the infinite series if possible.

Answer: 112.5 Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Evaluate a series.

169

27) Apply sigma notation to write the sum.

1+

+

+

+

Answer: Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 01 Learning Objective: Use summation (sigma) notation to represent a series.

© (2022) John Wiley & Sons, Inc. All rights reserved. Instructors who are authorized users of this course are permitted to download these materials and use them in connection with the course.

Except as permitted herein or by law, no part of these materials should be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise.

College Algebra, 5e (Young) Chapter 9 Sequences, Series, and Probability 9.2

Arithmetic Sequences and Series

1) Find the common difference d of the arithmetic series 5, 7, 9, 11, 13, ...

A) d = -2 B) d = 2 C) d = 8 D) d = 7 Answer: B Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Recognize an arithmetic sequence.

2) Find the common difference d of the arithmetic series 74, 70, 66, 62, 58, ...

A) d = -16 B) d = 16 C) d = 4 D) d = -4 Answer: D Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Recognize an arithmetic sequence.

3) Find the first four terms of the sequence

= -3n + 9, for n = 1, 2, 3, ... If the sequence is

arithmetic, find the common difference d.

A) = 12, = 15, = 18, = 21; not arithmetic B)

= 6,

= 3,

= 0, a4 = -3; not arithmetic 170

C)

= 12,

= 15,

D)

= 6,

= 3,

= 18, a4 = 21; d = 3 = 0, a4 = -3; d = -3

Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

171

4) Find the first four terms of the sequence

= 8(n - 7), for n = 1, 2, 3, ... If the sequence is

arithmetic, find the common difference d.

A) = -48, = -40, = -32, = -24; not arithmetic B)

= -48,

= -40,

= -32,

C)

= 48,

= 40,

= 32,

D)

= -48,

= -40,

= -24; d = 8 = 24; not arithmetic

= -32,

= -24; d = -8

Answer: B Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

5) Find the first four terms of the sequence

=

the common difference d.

A) = -2, = 4, = -6,

= 8; not arithmetic

B)

= -2,

= 4,

= -6,

= 8; d = 2

C)

= -2,

= 4,

= -6,

= 8; d = -2

D)

= 2,

= -4,

= 6,

= -8; not arithmetic

(2n). If the sequence is arithmetic, find

Answer: A Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Recognize an arithmetic sequence.

6) Find the general, or A)

= -4n - 6

B)

= 4n - 6

C)

= -6n - 4

D)

= -2n - 6

, term of the sequence given

= -2 and d = -6.

Answer: C Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

172

7) Find the general, or A)

= kn + (7 + k)

B)

= kn + (7 - k)

C)

= 7n + (7 - k)

D)

= kn - (7 - k)

, term of the sequence given

= 7 and d = k.

Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

8) Find the general, or A)

=

B)

= -10n -

C)

=

n+

D)

=

n-

, term of the sequence given

= -10 and

n-

Answer: D Diff: 2 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

9) Find the term of the sequence 8, 13, 18, 23, 28, ...

A) 45 B) 43 C) 38 D) 33 Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

173

10) Find the term of the sequence -6, 0, 6, 12, ...

A) 1164 B) 1170 C) 1176 D) -1200 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

11) Find the sum: A) 330 B) 226 C) 225 D) 275 Answer: D Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Evaluate a finite arithmetic series.

12) Find the sum: A) 247 B) 299 C) 210 D) 287 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Evaluate a finite arithmetic series.

13) A minor league baseball stadium has 160 seats in the front row, and each subsequent row has 15 more seats than the previous row. How many seats are in the stadium if there are 50 rows?

A) 223,125 seats B) 26,375 seats C) 910 seats D) 26,535 seats Answer: B Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

174

14) Find the common difference d of the arithmetic sequence 136, 120, 104, 88, 72, ...

Answer: -16 Diff: 1 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

15) Find term number 23 of the sequence 13, 26, 39, 52, 65, ...

Answer: 299 Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

16) An outdoor amphitheater has 90 seats in the front row and each subsequent row has 2 more seats than the previous row. How many seats are in in the amphitheater if there are 38 rows?

Answer: 4,826 Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

17) Find the sum.

-4 - 3 - 2 - ... + 31 A) 486 B) 472.5 C) 972 D) -486 Answer: A Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Evaluate a finite arithmetic series.

18) Find the sum of the first 65 terms of the series 7 + 14 + 21 + 28 + ...

Answer: 1,137.5 Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Evaluate a finite arithmetic series.

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19) For the arithmetic series with 13th term 66 and 34th term 192, find

and d and construct the

sequence by stating the general, or nth, term.

Answer: = -6; d = 6; = -6 + 6(n - 1) Diff: 3 Var: 1 Chapter/Section: Ch 09, Sec 02 Learning Objective: Find the general nth term of an arithmetic sequence.

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