39

CHAPTER 2, FORM A COLLEGE ALGEBRA AND TRIGONOMETRY 1. Match the set described in Column I with the correct interval notation from Column II. Choices in Column II may be used once, more than once, or not at all. I

II

a. Domain of f ( x)  x  3

A.

b. Range of f ( x)  x  3

B.

c. Domain of f  x  x  16

C.

d. Range of y  2 x2

D.

e. Domain of f ( x)  3 x  2

E.

f. Range of f ( x)  3 x  2

F.

g. Domain of f ( x)  x  2

G.

h. Range of f ( x)  x  3

H.

2

(, )

3,  0, 2 0,   3, 3  , 2  3,   7, 

i. Domain of y  2s 2

1. a. _____________ b. _____________ c. _____________ d. _____________

e. _____________

f. _____________

g. _____________

h. _____________

j. Range of f  x  x  7 2

i. _____________ j. _____________ The graph shows the line that passes through the points (  5,  3) and (  1, 4). Refer to it to answer Exercises 2–6.

40 2. What is the slope of the line?

2.

___________________________

3. What is the distance between the two points shown?

3.

___________________________

4. What are the coordinates of the midpoint of the segment joining the two points?

4.

___________________________

5. Find the standard form of the equation of the line.

5.

___________________________

6. Write the linear function defined by f ( x) ď&#x20AC;˝ ax ď&#x20AC;Ť b that has this line as its graph.

6.

___________________________

41 CHAPTER 2, FORM A Tell whether each graph is that of a function. Give the domain and the range. If it is a function, give the intervals where it is increasing, decreasing, or constant. 7.

7. ___________________________ ___________________________ ___________________________ ___________________________ ___________________________

8.

8.

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

2 3 9. Suppose point P has coordinates  ,  . 5 7 a. What is the equation of the vertical line through P?

9. a. __________________________

b. What is the equation of the horizontal line through P?

b. __________________________

10. Find the slope-intercept form of the equation of the line passing through (2, 5) and a. parallel to the graph of y  4x  7;

10. a. __________________________

b. perpendicular to the graph of y  4x  7.

b. __________________________

Graph each relation. 11. x  2 y  3  1

11.

42 CHAPTER 2, FORM A 12.

f  x  x  2

12.

13.

2 x  1 if x  0 f  x    3x  1 if x  0

13.

14. Explain how the graph of y   from the graph of y 

1 x  3  5 can be obtained 2

14. ___________________________

x.

15. Determine whether the graph of 2 x2  3 y 2  1 is symmetric with respect to

15. a. _________________________ b. _________________________

a. the x-axis,

c. _________________________

b. the y-axis, c. the origin. Given f  x  x2  1 and g  x  2 x  1, find each of the following. Simplify the expressions when possible. 16. 17.

 fg   x  f  g   x

18. the domain of

g f

16.

___________________________

17.

___________________________

18.

___________________________

43 CHAPTER 2, FORM A

19. 20.

f  x  h  f  x h

 f  g   0

 f 21.    2  g

19.

___________________________

20.

___________________________

21.

___________________________

22.

f

g   x

22.

___________________________

23.

f

g   2

23.

___________________________

24.

g

f   x

24.

___________________________

25.

g

f   2

25.

___________________________

44 NAME DATE

CHAPTER 2, FORM B COLLEGE ALGEBRA AND TRIGONOMETRY 1. Match the set described in Column I with the correct interval notation from Column II. Choices in Column II may be used once, more than once, or not at all. I

1. a. _____________ b. _____________

II

a. Domain of f ( x)  x  4

A.

b. Range of f ( x)  x  2

B.

c. Domain of f  x  3x2

C.

d. Range of f  x  x  5

D.

e. Domain of f ( x)  3 x  8

E.

f. Range of f ( x)  x  1

F.

g. Domain of f ( x)  x  2

G.

h. Range of f ( x)  x  5

H.

2

3

i. Domain of x  2 y

c. _____________

(, )

d. _____________

 2,  0, 2 0,   3, 3  , 2 5,   4, 

e. _____________

f. _____________

g. _____________

2

h. _____________

j. Range of x  2 y 2 i. _____________ j. _____________ The graph shows the line that passes through the points (  2,  1) and (4,  3). Refer to it to answer Exercises 2–6.

2. What is the slope of the line?

2.

___________________________

3. What is the distance between the two points shown?

3.

___________________________

4. What are the coordinates of the midpoint of the segment joining the two points?

4.

___________________________

5. Find the standard form of the equation of the line.

5.

___________________________

6. Write the linear function defined by f ( x)  ax  b that

6.

___________________________

has this line as its graph.

45 CHAPTER 2, FORM B Tell whether each graph is that of a function. Give the domain and the range. If it is a function, give the intervals where it is increasing, decreasing, or constant. 7.

7. ___________________________ ___________________________ ___________________________ ___________________________ ___________________________

8.

8.

Graph each relation. 9.

f  x   2  3x

10. f  x  

1 x 2

9.

10.

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

46 CHAPTER 2, FORM B 11.

 2 x if x  3  f  x   4 if  3  x  2  x  4 if x  2 

11.

5 7 12. Suppose point P has coordinates  ,   . 8 9 a. What is the equation of the vertical line through P?

12. a. __________________________

b. What is the equation of the horizontal line through P?

b. __________________________

13. Find the slope-intercept form of the equation of the line passing through  6, 3 and a. parallel to the graph of y  3x  12;

13. a. __________________________

b. perpendicular to the graph of y  3x  12.

14. Explain how the graph of y   from the graph of y 

1 x  4  2 can be obtained 3

b. __________________________

14. ___________________________

x.

15. Determine whether the graph of y 2  3x is symmetric

15. a. _________________________

with respect to

b. _________________________

a. the x-axis,

c. _________________________

b. the y-axis, c. the origin. Given f  x  2 x2  7 x  6 and g  x  3x  2, find each of the following. Simplify the expressions when possible. 16.

 fg   x

16.

___________________________

17.

 f  g   x

17.

___________________________

18.

___________________________

18. the domain of

g f

47 CHAPTER 2, FORM B 19. 20.

f  x  h  f  x h

 f  g  1

 g 21.    0  f

19.

___________________________

20.

___________________________

21.

___________________________

22.

f

g   x

22.

___________________________

23.

f

g  1

23.

___________________________

24.

g

f   x

24.

___________________________

25.

g

f  1

25.

___________________________

48 NAME DATE

CHAPTER 2, FORM C COLLEGE ALGEBRA AND TRIGONOMETRY 1. Match the set described in Column I with the correct interval notation from Column II. Choices in Column II may be used once, more than once, or not at all. I

1. a. _____________ b. _____________

II

a. Domain of f ( x)  x  2

A.

b. Range of f ( x)  x  4

B.

c. Domain of f  x  x2  1

C.

d. Range of f  x  x  16

D.

e. Domain of f ( x)  3 x  2

E.

f. Range of f ( x)  x  2

F.

g. Domain of f ( x)  x  3

G.

h. Range of f ( x)  x  3

H.

2

3

i. Domain of y  2 x

c. _____________

(, )

d. _____________

 4,  0, 2 0,   3, 3  , 3  1,   2, 

e. _____________

f. _____________

g. _____________

2

h. _____________

j. Range of y  x 2  3 i. _____________ j. _____________ The graph shows the line that passes through the points (  3,  5) and (3,  2). Refer to it to answer Exercises 2–6.

2. What is the slope of the line?

2.

___________________________

3. What is the distance between the two points shown?

3.

___________________________

4. What are the coordinates of the midpoint of the segment joining the two points?

4.

___________________________

5. Find the standard form of the equation of the line.

5.

___________________________

6. Write the linear function defined by f ( x)  ax  b that has this line as its graph.

6.

___________________________

49 CHAPTER 2, FORM C Tell whether each graph is that of a function. Give the domain and the range. If it is a function, give the intervals where it is increasing, decreasing, or constant. 7.

7. ___________________________ ___________________________ ___________________________ ___________________________ ___________________________

8.

8.

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

9. Suppose point P has coordinates  2 2,  5  . a. What is the equation of the vertical line through P? b. What is the equation of the horizontal line through P?

9. a. __________________________ b. __________________________

10. Find the slope-intercept form of the equation of the line passing through (4, 2 ) and a. parallel to the graph of x 

5 y  2; 4

b. perpendicular to the graph of x 

5 y  2; 4

10. a. __________________________ b. __________________________

50 CHAPTER 2, FORM C Graph each relation. 11. f  x  

1 x 1  2 2

11.

12.

f  x  2x  2

12.

13.

 x  1 if x  2 f  x    1 if x  2

13.

51 CHAPTER 2, FORM C 14. Explain how the graph of y  3 x  4  2 can be obtained

14. ___________________________

from the graph of y  x . 15. Determine whether the graph of y  3x2  7 is symmetric with respect to

15. a. _________________________ b. _________________________

a. the x-axis,

c. _________________________

b. the y-axis, c. the origin. Given f  x  3x2  2 and g  x  4 x  4, find each of the following. Simplify the expressions when possible. 16. 17.

 fg   x  g  f   x

18. f (2) 19. 20.

f  x  h  f  x h

 f  g   0

 f 21.    2  g

16.

___________________________

17.

___________________________

18.

___________________________

19.

___________________________

20.

___________________________

21.

___________________________

22.

 f  g   x

22.

___________________________

23.

f

g   x

23.

___________________________

24.

g

f   x

24.

___________________________

25.

g

f   0

25.

___________________________

52 NAME DATE

CHAPTER 2, FORM D COLLEGE ALGEBRA AND TRIGONOMETRY 1. Match the set described in Column I with the correct interval notation from Column II. Choices in Column II may be used once, more than once, or not at all. I

1. a. _____________ b. _____________

II

a. Domain of f ( x)  x  1

A.

b. Range of f ( x)  x  1

B.

c. Domain of f  x  x2  25

C.

d. Range of f  x  x  1

D.

e. Domain of f ( x)  3 x  2

E.

f. Range of f ( x)  x  2

F.

g. Domain of f ( x)  x  4

G.

h. Range of f ( x)  x  4

H.

2

3

i. Domain of y  2 x

c. _____________

 , 1  ,  0, 2 0,   3, 3  3,   1,   4, 

d. _____________

e. _____________

f. _____________

g. _____________

2

h. _____________

j. Range of y  x2  4 i. _____________ j. _____________ The graph shows the line that passes through the points (  7,  4) and (3,  2). Refer to it to answer Exercises 2–6.

2. What is the slope of the line?

2.

___________________________

3. What is the distance between the two points shown?

3.

___________________________

4. What are the coordinates of the midpoint of the segment joining the two points?

4.

___________________________

5. Find the standard form of the equation of the line.

5.

___________________________

6. Write the linear function defined by f ( x)  ax  b that

6.

___________________________

has this line as its graph.

53 CHAPTER 2, FORM D Tell whether each graph is that of a function. Give the domain and the range. If it is a function, give the intervals where it is increasing, decreasing, or constant. 7.

7.

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

8.

8.

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

Graph each relation. 9.

f  x  3  x  1

  x if x  0 10. f  x    2 x if x  0

9.

10.

54 CHAPTER 2, FORM D 11. Suppose point P has coordinates  3, 2.1 . a. What is the equation of the vertical line through P?

11. a. __________________________

b. What is the equation of the horizontal line through P?

b. __________________________

12. Find the slope-intercept form of the equation of the line passing through (1, 5 ) and a. parallel to the graph of x  

3 y  5; 4

b. perpendicular to the graph of x  

3 y  5; 4

13. Find the slope of the line through points (11, 5 ) and ( 8 , 6). from the graph of y 

b. __________________________

13. ___________________________

x.

14. Explain how the graph of y  3 x  4  2 can be obtained from the graph of y 

12. a. __________________________

14. ___________________________

x.

15. Determine whether the graph of xy  4 is symmetric

15. a. _________________________

with respect to

b. _________________________

a. the x-axis,

c. _________________________

b. the y-axis, c. the origin. Given f  x  2x3  3x  1 and g  x  2 x  1, find each of the following. Simplify the expressions when possible. 16.

 f  g   x

 f 17.    x   g

16.

___________________________

17.

___________________________

18.

f  0

18.

___________________________

19.

f  x  h  f  x h

19.

___________________________

20.

 g  f   0

20.

___________________________

21.

 fg   1

21.

___________________________

22.

f

22.

___________________________

g   x

55 CHAPTER 2, FORM D 23.

f

g   2

23.

___________________________

24.

g

f   x

24.

___________________________

25.

g

f   2

25.

___________________________

56 CHAPTER 2, FORM E COLLEGE ALGEBRA AND TRIGONOMETRY

NAME DATE

Choose the best answer. 1a. Which of the following is the domain of f  x   3  x ? a. c.

0, 3 3, 

 , 3  , 

b. d.

1b. Which of the following is the range of f  x  x2  49 ? a. c.

 49,   7, 7

d.

c.

 ,  0, 

d.

c.

 1,1 0, 

d.

c.

 ,   0, 

1d. _________________

0,1 1,  

b.

1e. Which of the following is the domain of x  y 2 ? a.

1c. __________________

 , 6 6, 

b.

1d. Which of the following is the range of f  x   x  1? a.

1b. __________________

 7,  0, 

b.

1c. Which of the following is the domain of f  x  3 x  7 ? a.

1a. __________________

1e. __________________

0,   , 0

b. d.

The graph shows the line that passes through  5, 8 and  4, 3 . Refer to it to answer Exercises 2-6.

2. What is the slope of the line? a.

13 7

b.

2. ___________________

11 9

11 d. 0 9 3. What is the distance between the two points shown? c.

a.

26

b.

c.

202

d.

2 5 122

3. ___________________

57 CHAPTER 2, FORM E 4. What are the coordinates of the midpoint of the segment joining the two points? a.

 1 5   ,  2 2

b.

 9 11   ,  2 2

c.

 3 1  ,  2 2

d.

 1, 5

5. Find the standard form of the equation of the line. a. 11x  9 y  127 b. 11x  9 y  17 c.

11x  9 y  17

d.

c.

11 17 x 9 9 11 127 f  x  x  9 9 f  x 

b. d.

b. c. d.

6. ___________________

11 17 x 9 9 11 127 f  x  x 9 9 f  x  

Tell whether each graph is that of a function. Give the domain and range. 7.

a.

5. ___________________

11x  9 y  127

6. Find the standard form of the equation of the line. a.

4. ___________________

7. ___________________

Function; domain:  5, 7 ; range:  1, 3

Function; domain:  ,  ; range:  1, 3

Function; domain:  1, 3 ; range:  5, 7

Not a function; domain:  5, 7 ; range:  1, 3

8.

8. ___________________

a.

Not a function; domain:  ,  ; range:  2, 

b.

Not a function; domain:  5, 5 ; range:  3, 

c.

Function; domain:  ,  ; range:  2, 

58

d.

Function; domain:  ,  ; range:  3, 

59 CHAPTER 2, FORM E 9. Suppose point P has coordinates  6,1 .

9. ___________________

What is the equation of the horizontal line through P? a. c.

x  6 x 1

y 1 y6

b. d.

10. Find the slope-intercept form of the equation of the line passing. 1 19 through  2, 5 perpendicular to the graph of y   x  . 8 4

a.

y  8x  21

b.

c.

y  8x  13

d.

10. __________________

1 x3 3 1 y   x3 3

y

Graph each function. 11. f  x   2 x  1  2

11. __________________

a.

b.

c.

d.

60 CHAPTER 2, FORM E 12. f  x  

1 x 2

12. __________________

a.

b.

c.

d.

if x  2 2  13. f  x    1  x  1 if x  2   2

13. __________________

a.

b.

c.

d.

61 CHAPTER 2, FORM E 14. Explain how the graph of y  x  2  5 can be obtained from the graph of y  a. b. c. d.

x.

Translate 2 unit to the right and 5 units up. Translate 2 unit to the right and 5 units down. Translate 2 unit to the left and 5 units up. Translate 2 unit to the left and 5 units down.

15. Determine the symmetries of the graph of the relation x2  2 xy  y 2  5. a. c.

14. __________________

x-axis only origin only

15. __________________

b. y-axis only d. x-axis, y-axis, and origin

Given f  x  5x  4 and g  x  x2  3, find each of the following. Simplify the expressions when possible. 16.

17.

 fg   x a.

x3  4 x2  12

b. 5x3  4 x2  15x  12

c.

5x3  4 x2  3x  12

d. 5x3  4 x2  5x  12

 g  f   x

20.

17. __________________

a.

x 2  5x  7

b. x2  5x  7

c.

 x2  5x  1

d. x2  5x  1

18. The domain of

19.

16. __________________

g f

18. __________________

a.

4  4    ,    ,  5 5

5  5   b.  ,    ,   4  4 

c.

1  1    ,    ,  3 3

d.

 , 

f  x  h  f  x h

19. __________________

a.

h

b. 5

c.

5x  2h

d. 5x  2h  4

 f  g   1 a. c.

1 2

20. __________________ b. 5 d. 5

62 CHAPTER 2, FORM E

 f 21.    0  g

22.

23.

24.

25.

21. __________________

a.

3 4

b.

1 4

c.

4 3

d.

15 2

g

f   x

a.

25x2  40 x  19

b. 25x2  40 x  19

c.

25x2  40 x  19

d. 25x2  40 x  19

g

f  1

a. c.

6 0

f

g   x

a.

5x2  11

b. 5x2  11

c.

5x2  19

d. 5x2  12

f

g   0

a.

1 11

c.

22. __________________

22. __________________ b. 4 d. 1 24. __________________

25. __________________ b. 0 d. 15

63 CHAPTER 2, FORM F COLLEGE ALGEBRA AND TRIGONOMETRY

NAME DATE

Choose the best answer. 1a. Which of the following is the domain of f  x  x  1 ? a. c.

0,1 1,  

 ,1  , 

b. d.

1b. Which of the following is the range of f  x   x2  4? a. c.

2,   4, 4

b. d.

c.

 ,  0, 

d.

c.

 2, 2  2, 

d.

c.

 ,   0, 

1d. _________________

0, 2 0, 

b.

1e. Which of the following is the domain of x  y 2 ? a.

1c. __________________

 , 3 3, 

b.

1d. Which of the following is the range of f  x   x  2? a.

1b. __________________

 4,  0, 

1c. Which of the following is the domain of f  x  3 x  7 ? a.

1a. __________________

1e. __________________

0,   , 0

b. d.

The graph shows the line that passes through  7, 4 and  3, 2 . Refer to it to answer Exercises 2-6.

2. What is the slope of the line? a.

0

b.

2. ___________________

1 5

1 d. 5 5 3. What is the distance between the two points shown? c.

a.

122

b.

2 26

c.

2 13

d.

2 34

3. ___________________

64 CHAPTER 2, FORM F 4. What are the coordinates of the midpoint of the segment joining the two points? a. c.

 1 11  ,   2 2

 5, 1

b.

 2, 1

d.

 2, 3

5. Find the standard form of the equation of the line. a. 5x  y  17 b. 5x  y  17 c.

x  5 y  13

d.

f  x 

1 13 x 5 5

b.

f  x  5x  17

d.

f  x 

a.

not a function; domain:  , 0   0,  ; range:  , 2   0, 

b.

not a function; domain:  ,  ; range:  , 

c.

not a function; domain:  , 0   0,  ; range:  , 

d.

not a function; domain:  , 0   0,  ; range:  , 2   2, 

8.

a. b. c. d.

6. ___________________

f  x  5x  17

1 13 x 5 5 Tell whether each graph is that of a function. Give the domain and range. 7. c.

5. ___________________

x  5 y  13

6. Find the standard form of the equation of the line. a.

4. ___________________

7. ___________________

8. ___________________

not a function; domain:  2,1 ; range:  ,  not a function; domain:  7, 5 ; range:  2,1

not a function; domain:  7, 5 ; range:  ,  not a function; domain:  2,1 ; range:  7, 5

65 CHAPTER 2, FORM F 9. Suppose point P has coordinates  3, 6 .

9. ___________________

What is the equation of the horizontal line through P? a. x  3 b. y  3 c.

x6

y6

d.

10. Find the slope-intercept form of the equation of the line passing. 1 1 through 1, 2 perpendicular to the graph of y   x  . 8 3

a.

y  8x  3

b.

c.

y  8x  3

d.

10. __________________

1 1 x 8 3 1 17 y   x 8 8 y

Graph each relation. 11. f  x  

1 x 1 2

11. __________________

a.

b.

c.

d.

66 CHAPTER 2, FORM F 12. f  x  

1 x 2 2

12. __________________

a.

b.

c.

d.

 2 x if x  1 13. f  x     x  3 if x  1

13. __________________

a.

b.

c.

d.

14. Explain how the graph of y  x  3  1 can be obtained from the graph of y  x . a. Translate 3 units to the right and 1 units up. b. Translate 3 units to the right and 1 units down. c. Translate 3 units to the left and 1 units up. d. Translate 3 units to the left and 1 units down.

14. __________________

67 CHAPTER 2, FORM F 15. Determine the symmetries of the graph of the relation 4 x2  9 y 2  36. a. c.

x-axis only Origin only

15. __________________

b. y-axis only d. x-axis, y-axis, and origin

Given f  x  6 x2  5x  6 and g  x  2 x  8, find each of the following. Simplify the expressions when possible. 16. f  3 a. c.

17.

18.

d. 51

17. __________________

a.

12x  6h  5

b. 12x  6h  5

c.

12 x  6h  5

d. 12x  6h  5

f c.

20.

b. 21

f  x  h  f  x h

a.

19.

9 33

16. __________________

 3 g    2

131 181

18. __________________ b. 119 d. 169

 f  g   x

19. __________________

a.

6 x2  7 x 14

b. 6 x2  7 x 14

c.

6 x2  7 x  2

d. 6 x2  3x  2

 f  g   0 a. c.

15 27

20. __________________ b. 14 d. 1

68