Test Bank for Precalculus with Limits A Graphing Approach Texas Edition 6th Edition by Larson IBSN 9781285867717 Full clear download (no formatting errors ) at: http://downloadlink.org/p/test-bank-for-precalculus-with-limits-a-graphingapproach-texas-edition-6th-edition-by-larson-ibsn-9781285867717/ Solutions Manual for Precalculus with Limits A Graphing Approach Texas Edition 6th Edition by Larson IBSN 9781285867717 Full clear download (no formatting errors ) at: http://downloadlink.org/p/solutions-manual-for-precalculus-with-limits-agraphing-approach-texas-edition-6th-edition-by-larson-ibsn-9781285867717/ Name:

Date:

Chapter 2: Polynomial and Rational Functions 1. Use long division to divide. ( x4 – x 2 – 5) ÷ ( x2 + 4 x – 1) A) B) C) D) E)

x2 – 4 x + 4 x 2 + 4x – 4 –68x + 11 x 2 + 4x – 1 –5x − 1 x 2 + 4x – 4 + 2 x + 4x – 1 4 x 2 – 4x + 4 − 2 x – 4x + 4 x 2 – 4x + 16 +

2. Write f ( x) = x 4 – 12 x 3 + 59x 2 – 138x + 130 as a product of linear factors. A) ( x − 3 − i ) ( x − 3 + 2 i ) ( x − 3 − 2 i ) ( x − 2 + i ) B) C) D) E)

( x − 3 − i )( x − 3 + i) ( x − 2 − i)( x − 2 + i) ( x − 3 − i) ( x − 3 + i) ( x + 3 − 2 i)( x − 2 + i) ( x − 3 + i ) ( x − 3 − i ) ( x – 2 + 3i ) ( x – 2 − 3 i ) ( x − 3 + i)( x − 3 − i)( x – 3 + 2i)( x – 3 − 2i)

3. Find the zeros of the function below algebraically, if any exist.

A) B) C) D) E)

f ( x) = x5 – 5x3 + 4 x –4, –1, 1, 4 –4, –2, 2, 4 –2, –1, 0, 1, 2 –4, –2, 0, 2, 4 No zeros exist.

69 use.

4. Find two positive real numbers whose product is a maximum and whose sum of the first number and four times the second is 200 . A) 160, 10 B) 116, 21 C) 108, 23 D) 100, 25 E) 76, 31

A) B) C) D) E)

x2 . x 2 + 16

horizontal: y = 4 ; vertical: x = –4 horizontal: x = 1 ; vertical: none horizontal: y = –4 ; vertical: x = 1 horizontal: y = 1; vertical: none horizontal: none; vertical: none

6. Find a polynomial function with following characteristics.

A) B) C) D) E)

Degree: 4 Zero: –1 , multiplicity: 2 Zero: –3 , multiplicity: 2 Falls to the left, Falls to the right Absolute value of the leading coefficient is one y = x 4 – 4 x3 + 22 x 2 + 24 x + 3 y = − x 4 – 4x3 + 12x 2 + 9 y = x 4 – 6x3 – 18x 2 + 10 x + 3 y = − x 4 – 8x3 – 22x 2 – 24 x – 9 y = − x 4 – 8x3 – 24x + 9

7. A polynomial function f has degree 3, the zeros below, and a solution point of f ( –3) = –4. Write f in completely factored form. –4, –3 + 2i A) f ( x ) = ( x + 3 ) ( x + 4 – 2i ) ( x + 4 + 2i ) B)

f ( x ) = – ( x + 4 ) ( x + 2 – 3i ) ( x + 2 + 3i )

C)

f ( x ) = ( x + 4 ) ( x + 2 – 3i ) ( x + 2 + 3i )

D)

f ( x ) = – ( x + 4 ) ( x + 3 – 2i ) ( x + 3 + 2i )

E)

f ( x ) = ( x + 4 ) ( x + 3 – 2i ) ( x + 3 + 2i )

© 2014 Cengage Learning. All Rights Reserved. This content is not yet final and Cengage Learning does not guarantee this page will contain current material or match the published product.

5. Determine the equations of any horizontal and vertical asymptotes of f ( x) =

© 2014 Cengage Learning. All Rights Reserved. This content is not yet final and Cengage Learning does not guarantee this page will contain current material or match the published product.

8. The interest rates that banks charge to borrow money fluctuate with the economy. The interest rate charged by a bank in a certain country is given in the table below. Let t represent the year, with t = 0 corresponding to 1986. Use the regression feature of a graphing utility to find a quadratic model of the form y = at 2 + bt + c for the data. Year Percent t y 1986 12.4 1988 9.7 1990 7.3 1992 6.3 1994 9.7 1996 11.6 2 A) y = –2.13t +12.61t + 0.21 B) y = 12.61t 2 + 0.21t – 2.13 C) y = 0.21t 2 – 2.13t +12.61 D) y = 0.17t 2 – 2.58t +10.59 E) y = 0.25t 2 – 1.73t +14.37

9. Find the zeros of the function below algebraically, if any exist.

A) B) C) D) E)

f ( x) = 25x3 – 60 x 2 + 36x 6 − and 0 5 6 0 and 5 6 6 − , 0, and 5 5 6 6 − and 5 5 No zeros exist.

10. Determine the zeros (if any) of the rational function f ( x) = A) x = –5 8 8 B) x = – , x = 5 5 C) x = –64, x = 64 D) x = –8, x = 8 E) no zeros 71 use.

x 2 – 64 . x+5

11. The graph of the function

is shown below. Determine the domain.

A) B) C) D) E)

12. Which of the given graphs is the graph of the polynomial function below? h ( x ) = x5 –

Graph 1 :

Graph 2 :

Graph 3 :

73 use.

3 3 1 x – x 2 2

Graph 5 :

A) B) C) D) E)

Graph 2 Graph 5 Graph 4 Graph 1 Graph 3

13. Perform the addition or subtraction and write the result in standard form. − ( 7.2 – 12.3 i ) − 8.1 − –1.21

(

A) –15.3 +13.4 i B) 0.9 +13.4 i C) –0.9 +11.2 i D) –15.3 +11.2 i E) 15.3 + 13.4 i

)

© 2014 Cengage Learning. All Rights Reserved. This content is not yet final and Cengage Learning does not guarantee this page will contain current material or match the published product.

Graph 4 :

14. Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one.

A)

–3, –1, 0, 1, 3 f ( x ) = x + 7 x – 19x – 32 x + 48x

B)

f ( x ) = x5 + 7 x 4 – 19x3 + 32 x 2 + 48x

C)

f ( x ) = x5 + 4x 4 – 13x3 + 3x 2 +12x

D)

f ( x ) = x5 + 5x 4 – 13x3 + 27 x 2 + 36 x

E)

f ( x ) = x5 – 10x3 + 9x

5

4

3

2

15. Find the zeros of the function below algebraically, if any exist. f ( x ) = x 6 – 9 x3 + 8 A) 1 and 2 B) –4 and 1 C) –4 and 2 D) –4, –1, 1, and 4 E) –4, –2, 2, and 4

16. Identify any horizontal and vertical asymptotes of the function below. 2x – 8 x +6 vertical asymptotes: x = –2 and x = 2; horizontal asymptotes: y = –6 and y = 6 vertical asymptotes: x = –2 and x = 2; horizontal asymptotes: none vertical asymptotes: x = –6 and x = 6; horizontal asymptotes: none vertical asymptotes: none; horizontal asymptotes: y = –2 and y = 2 vertical asymptotes: x = –6 and x = 6; horizontal asymptotes: y = –2 and y = 2 f ( x) =

A) B) C) D) E)

75 use.

17. Find all the rational zeros of the function f ( x) = –2 x5 – 11x 4 – 19 x3 – 17 x 2 – 17 x – 6 . 1 A) x = , –3, –1 2 2 B) x = – ,1, –2 3 1 3 C) x = – , , –2 2 2 1 3 D) x = – , 2 2 1 E) x = – , –3, –2 2 18. Find real numbers a and b such that the equation a + b i = –10 + 10 i is true. A) a = 10, b = –10 B) a = –10, b = –10 C) a = 10, b = 10 D) a = –10, b = 10 E) a = –20, b = 0

19. Use long division to divide. ( x3 + 3x2 + x + 3) ÷ ( x + 3) A)

x2 + 3

B)

x 2 + 6x + 17 −

C) D) E)

53 x+3 48 x 2 + 6x + 19 + x+3 2 x + 6 x + 17 x2 + 1

20. Find two positive real numbers whose product is a maximum and whose sum is 146 . A) 71, 75 B) 73, 73 C) 78, 68 D) 82, 64 E) 61, 85

Answer Key 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

C E C D D D D C B D A C A E A D E D E B

77 use.

Name:

Date:

1. Describe the right-hand and the left-hand behavior of the graph of 4 t ( x) = – ( x3 + 5x 2 + 8x + 1) . 7 Because the degree is odd and the leading coefficient is positive, the graph falls to A) the left and falls to the right. Because the degree is odd and the leading coefficient is negative, the graph rises to B) the left and falls to the right. Because the degree is odd and the leading coefficient is negative, the graph falls to C) the left and rises to the right. Because the degree is odd and the leading coefficient is positive, the graph rises to D) the left and rises to the right. Because the degree is even and the leading coefficient is negative, the graph rises E) to the left and falls to the right. 2 is a root of 25x3 – 70x 2 + 44 x – 8 = 0 , use synthetic division to factor the 5 polynomial completely and list all real solutions of the equation. 2 2 A) ( 5x – 2 ) ( 5x + 2 ) ( x – 2 ) ; x = , – , 2 5 5 2 2 B) ( 5x + 2 ) ( x – 2 ) ; x = – , 2 5 2 2 C) ( 5x – 2 ) ( x – 2 ) ; x = , 2 5 2 2 D) ( 5x + 2 ) ( x – 2 ) ; x = – 5 , 2 2 2 E) ( 5x – 2 ) ( x – 2 ) ; x = 5 , 2

2. If x =

2

2

3. Simplify ( 3 – 6i ) − ( 3 + 6 i ) and write the answer in standard form. A) B) C) D) E)

0 –72 i 18 – 72 i 18 + 72 i 6 – 24 i

6x + 6 . x 2 – 6x all real numbers except x = −1, x = 0, and x = 6 all real numbers except x = 0 and x = 6 all real numbers except x = –6 and x = −1 all real numbers except x = 6 all real numbers

4. Determine the domain of f ( x) = A) B) C) D) E)

5. Suppose the IQ scores (y, rounded to the nearest 10) for a group of people are summarized in the table below. Use the regression feature of a graphing utility to find a quadratic function of the form y = ax 2 + bx + c for the data. IQ Score Number of People y x 70 50 80 76 90 89 100 93 110 74 120 53 130 16 2 A) y = –0.04 x +15.08x – 411.58 B) y = –0.06 x 2 +12.06 x – 484.21 C) D) E)

y = –0.08x 2 +10.98x – 508.43 y = –0.07 x 2 +13.63x – 460 y = –0.09 x 2 + 8.56x – 556.85

6. Simplify f below and find any vertical asymptotes of f. x 2 – 25 f ( x) = x+5 A) f ( x ) = x + 5, x ≠ 5; vertical asymptotes: none B)

f ( x ) = x – 5, x ≠ –5; vertical asymptotes: none

C)

f ( x ) = x – 5, x ≠ 5; vertical asymptotes: none

D)

f ( x ) = x + 5, x ≠ –5; vertical asymptotes: x = –5

E)

f ( x ) = x – 5, x ≠ 5; vertical asymptotes: x = 5

79 use.

7. Find the quadratic function f whose graph intersects the x-axis at ( 2, 0 ) and ( 3, 0 ) and the y-axis at ( 0, –18) . A)

f ( x ) = 3x 2 + 3x + 9

B)

f ( x ) = –3x 2 +15x – 18

C)

f ( x ) = –3x 2 – 3x + 6

D)

f ( x ) = 3x 2 – 3x – 18

E)

f ( x ) = 3x 2 – 15x – 18

8. Using the factors ( –5x + 2 ) and ( x – 1) , find the remaining factor(s) of f ( x) = 10x 4 + 31x3 – 84x 2 + 53x – 10 and write the polynomial in fully factored form. A)

f ( x) = ( –5x + 2 ) ( –5x + 2 ) ( 2 x – 1) ( x – 1)

B)

f ( x) = ( –5x + 2 ) ( – x – 5 ) ( 2x – 1) ( x – 1)

C)

f ( x) = ( –5x + 2 ) ( 2 x – 1) ( x + 1)

D)

f ( x) = ( –5x + 2 ) ( – x + 5) ( x + 1)

E)

f ( x) = ( –5x + 2 ) ( x – 1)

2

2

2

4 + 3i and write the answer in standard form. 5 + 2i 26 7 – + i 29 29 26 7 – i 29 29 26 7 + i 29 29 7 26 + i 29 29 7 26 – i 29 29

9. Simplify A) B) C) D) E)

2

10. Write the complex conjugate of the complex number –5 − 10 i . A)

5 − 10 i

B)

–5 − –10 i

C)

5 − –10 i

D)

–5 + 10 i

E)

5 + 10 i

11. Determine the value that f ( x) =

4x − 6 approaches as x increases and decreases in x2 − 7

magnitude without bound. A) 8 B) 6 C) 4 D) 2 E) 0 12. Find all real zeros of the polynomial f ( x) = x 4 + 13x3 + 40x 2 and determine the mutiplicity of each. A) x = 0 , multiplicity 2; x = –8 , multiplicity 1; x = –5 , multiplicity 1 B) x = 8 , multiplicity 2; x = 5 , multiplicity 2 C) x = 0 , multiplicity 2; x = 8 , multiplicity 1; x = 5 , multiplicity 1 D) x = –8 , multiplicity 2; x = –5 , multiplicity 2 x = 0 , multiplicity 1; x = 8 , multiplicity 1; x = –8 , multiplicity 1; x = 5 , E) multiplicity 1 13. Given 3 + i is a root, determine all other roots of f ( x) = x 4 – 10 x3 + 42x 2 – 88x + 80 . A) x = 3 + i, 2 ± 2 i, 2 − i B) x = 3 − i, 2 ± i C) x = 3 − i, 2 − 2 i, 2 + i D) x = 3 − i, – 2 ± 2 i E) x = 3 − i, 2 ± 2 i

81 use.

14. Determine the zeros (if any) of the rational function f ( x) =

x2 – 9 . x–2

A) x = 2 3 3 B) x = , x = – 2 2 C) x = –9, x = 9 D) x = –3, x = 3 E) no zeros 15. Determine the zeros (if any) of the rational function g ( x) = A) x = –1, x = 1 B) x = 1 C) x = − 5, x = 5, x = 1 D) x = − 5, x = 5, x = –1, x = 1 E) no zeros

16. Match the equation with its graph.

A)

B)

x3 – 1 . x2 + 5

C)

D)

E)

17. Determine the zeros (if any) of the rational function g ( x) = 7 + x = − 7, x = 7 x = –3 3 3 C) x = – , x = 7 7 D) x = –7, x = 7 E) no zeros A) B)

3 . x +7 2

Test Bank for Precalculus with Limits A Graphing Approach Texas Edition 6th Edition by Larson IBSN 9781285867717 Full clear download (no formatting errors ) at: http://downloadlink.org/p/test-bank-for-precalculus-with-limits-a-graphingapproach-texas-edition-6th-edition-by-larson-ibsn-9781285867717/ Solutions Manual for Precalculus with Limits A Graphing Approach Texas Edition 6th Edition by Larson IBSN 9781285867717 Full clear download (no formatting errors ) at: http://downloadlink.org/p/solutions-manual-for-precalculus-with-limits-agraphing-approach-texas-edition-6th-edition-by-larson-ibsn-9781285867717/ People also search: precalculus with limits a graphing approach texas edition pdf precalculus with limits a graphing approach sixth edition precalculus with limits texas edition pdf precalculus with limits texas edition answers precalculus with limits a graphing approach 6th edition solution manual precalculus with limits a graphing approach 5th edition pdf precalculus with limits a graphing approach 6th edition pdf chapter 1 larson's precalculus with limits a graphing approach 6e

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