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Test bank for A Graphical Approach to Precalculus with Limits A Unit Circle Approach 4th Edition by Hornsby

Test bank for A Graphical Approach to Precalculus with Limits

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or

answers the question.

Determine the intervals of the domain over which the function is continuous.

1) 1)

C) D) [0, ∞)

2) 2)

A) (-∞, ∞) B) (-∞, 0] C) [0, ∞) D) (0, ∞)

3) 3)

A) (-∞, ∞) B)

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Test bank for A Graphical Approach to Precalculus with Limits A Unit Circle Approach 4th Edition by Hornsby

A) (-∞, 0) B) (-∞, 0); (0, ∞)

C) (-∞, ∞) D) (0, ∞)

4)

_

A) (-∞, 2); ( 2, ∞) B) (-∞, ∞)

C) ( 2, ∞)

5)

D) (-∞, 2]

5)

A) (-∞, -2); ( -2, ∞) B) (-∞, ∞)

C) (-∞, 2); ( 2, ∞) D) (0, ∞)

6) 6)

A) (-∞, 4); ( 4, ∞) B) (-∞, 2); ( 2, ∞)

C) (-∞, -2); ( -2, ∞) D) (-∞, ∞)

7)

_

A) [ 2, ∞) B) [0, 2) C) [ -2, ∞) D) [0, ∞)

8) 8)

A) ( 4, ∞) B) (0, 4) C) (-∞, ∞) D) (0, ∞)

Determine the intervals on which the function is increasing, decreasing, and constant.

9) 9)

A) Increasing on [1, ∞); Decreasing on (-∞, 1]

B) Increasing on [-1, ∞); Decreasing on (-∞, -1]

C) Increasing on (-∞, -1]; Decreasing on [-1, ∞)

D) Increasing on (-∞, 1]; Decreasing on [1, ∞)

10)

7)

10)

A) Increasing on (-∞, 0]; Decreasing on (-∞, 0]

B) Increasing on (∞, 0]; Decreasing on [0, -∞)

C) Increasing on (-∞, 0]; Decreasing on [0, ∞)

D) Increasing on [0, ∞); Decreasing on (-∞, 0]

11) 11)

A) Increasing on (∞, 0]; Decreasing on [0, -∞)

B) Increasing on [0, ∞); Decreasing on (-∞, 0]

C) Increasing on (-∞, 0]; Decreasing on (-∞, 0]


12) 12)

A) Increasing on (-∞, -2]; Decreasing on [ -2, ∞)


C) Increasing on [-2, ∞); Decreasing on [ -2, ∞)

D) Increasing on (-∞, -2]; Decreasing on (-∞, -2]

13)

A) Increasing on (-∞, 0]; Decreasing on [0, ∞)

B) Decreasing on (-∞, ∞)

C) Increasing on (-∞, ∞)


14) 14)

A) Increasing on [ 4, ∞); Decreasing on [ -4, ∞); Constant on [ -4, 4]

B) Increasing on [ 4, ∞); Decreasing on (-∞, -4]; Constant on [ -4, 4]

C) Increasing on (-∞, 4]; Decreasing on (-∞, -4]; Constant on [4, ∞)

D) Increasing on (-∞, 4]; Decreasing on [ -4, ∞); Constant on [4, ∞)

15) 15)

A) Increasing on [-1, 0] and [3, 5]; Decreasing on [0, 3]; Constant on

[-5, -3]

B) Increasing on [-2, 0] and [3, 5]; Decreasing on [1, 3]; Constant on

C) Increasing on [1, 3]; Decreasing on [-2, 0] and [3, 5]; Constant on

[2, 5]

13)

D) Increasing on [-2, 0] and [3, 4]; Decreasing on [-5, -2] and [1, 3]

16) 16)

A) Increasing on [-3, 0]; Decreasing on [-5, -3) and [2, 5]; Constant on

[0, 2]

B) Increasing on [-3, -1]; Decreasing on [-5, -2] and [2, 4]; Constant on

[-1, 2]

C) Increasing on [-3, 1]; Decreasing on [-5, -3] and [0, 5]; Constant on

[1, 2]

D) Increasing on [-5, -3] and [2, 5]; Decreasing on [-3, 0]; Constant on

[0, 2]

Find the domain and the range for the function.

17) 17)

B)

D: , R: [0, ∞)

D) D: (-∞, ∞), R: (-∞, ∞)

18)

A)

D: [0, ∞), R:

C)

D: , R: (-∞, 0]

18)

A) D: (-∞, 0], R: (-∞, 0] B) D: (0, ∞), R: (0, ∞)

C) D: [0, ∞), R: [0, ∞)

19)

D) D: (-∞, ∞), R: (-∞, ∞)

19)

A) D: [ 4, ∞), R: [0, ∞) B) D: (0, ∞), R: (-∞, 0)

C) D: ( 4, ∞), R: [0, ∞)

20)

D) D: [0, ∞), R: (-∞, 0]

20)

A) D: (0, ∞), R: (-∞, 15] B) D: (-∞, ∞), R: [-6, ∞)

C) D: (-∞, ∞), R: (-∞, ∞) D) D: (-∞, 0), R: (-∞, 0)

21)

21)

A) D: (-∞, 6], R: [6, ∞) B) D: (-∞, ∞), R: [0, ∞)

C) D: (-∞, 6], R: [0, ∞)

22)

D) D: [0, ∞), R: (-∞, 6]

22)

A) D: (-∞, ∞), R: (-∞, ∞)

B) D: (-∞, -8) ∪ (-8, ∞), R: (-∞, ∞)

C) D: (-∞, 8) ∪ (8, ∞), R: (-∞, 1) ∪ (1, ∞)

D) D: (0, ∞), R: (1, ∞)

23) 23)

A) D: (-∞, ∞), R: (-∞, ∞)

B) D: (-∞, -2) ∪ (-2, ∞), R: (-∞, -4) ∪ (-4, ∞)

C) D: (-∞, 4) ∪ (4, ∞), R: (-∞, 2) ∪ (2, ∞)

D) D: (-∞, 2) ∪ (2, ∞), R: (-∞, 4) ∪ (4, ∞)

24)

A) D: [0, ∞), R: [5, ∞) B) D: [5, ∞), R: [0, ∞)

C) D: [0, ∞), R: [0, ∞)

25)

D) D: [ -5, ∞), R: (-∞, 0]

25)

A) D: (-∞, ∞), R: (-∞, ∞) B) D: (0, ∞), R: [0, ∞)

C) D: (4, ∞), R: [0, ∞) D) D: ( 5, ∞), R: (-∞, 0]

Determine if the function is increasing or decreasing over the interval indicated.

26) f(x) = 7x - 5; (-∞, ∞) 26)

A) Increasing B) Decreasing

27)

f(x) = - x; (1, ∞)


27)

28) f(x) = - 2x + 1; (1, ∞)

28)


29)

f(x) = ; (3, ∞) 29)


30)

f(x) = ; (-∞, 0)


30)

31) f(x) = ; (-∞, 4) 31)


24)

32) f(x) = ∣ x - 8∣ ; (-∞, 8) 32)


33)

f(x) = + 7; (0, ∞)


33)

34) f(x) = - ; (-3, ∞) 34)


Determine if the graph is symmetric with respect to the x-axis, y-axis, or origin.

35) 35)

A) y-axis B) y-axis, origin

C) Origin D) x-axis, origin

36) 36)

A) y-axis B) y-axis, origin

C) x-axis, origin D) x-axis

37)

A) Origin B) x-axis, y-axis, origin

C) x-axis D) x-axis, origin

38) 38)

A) y-axis B) x-axis, origin

C) Origin D) x-axis

39) 39)

A) No symmetry B) y-axis

C) Origin D) x-axis

Based on the ordered pairs seen in the pair of tables, make a conjecture as to whether the

function defined in Y1 is even, odd, or neither even nor odd.

40)

37)

A) Neither even nor odd

B) Even

C) Odd

41) 41)


B) Odd

C) Even

42)

40)

A) Even

B) Neither even nor odd

C) Odd

43) 43)

A) Odd


C) Even

44)

42)


B) Odd

C) Even

45) 45)


B) Odd

C) Even

46)

44)

A) Even

B) Odd

C) Neither even nor odd

47) 47)


B) Odd

C) Even

48)

46)

A) Odd


C) Even

49) 49)


B) Odd

C) Even

Determine whether the function is even, odd, or neither.

50) f(x) = + 2

50)

A) Even B) Odd C) Neither

51) f(x) = (x + 8)(x + 5) 51)


48)

52) f(x) = -3 + 3x

52)


53)

f(x) = -4 - 5 53)


54)

f(x) = + + 6 54)


55)

f(x) = + 4x - 2 55)


56) f(x) = 56)


57)

f(x) = -


57)

Determine whether the graph of the given function is symmetric with respect to the y-axis,

symmetric with respect to the origin, or neither.

58) f(x) = - 4

58)

A) y-axis B) Origin C) Neither

59) f(x) = + 5 59)


60) f(x) = 3 60)


61)

f(x) = + 5 61)


62)

f(x) = -2 + 9x 62)


63)

f(x) = 3 + 2 63)


64)

f(x) = + - 2 64)


65)

f(x) = - 6x + 9 65)


66) f(x)

= x

66)

+


Provide an appropriate response.

67)

True or False: The function y = is not continuous at x = 7.

A) True B) False

68) Sketch the graph of f(x) = . At which of these points is the function

increasing?

A) 3 B) 5 C) -3 D) 0

69) True or False: A continuous function cannot be drawn without lifting

the pencil from the paper.

A) True B) False

67)

68)

69)

70) What symmetry does the graph of y = f(x) exhibit? 70)

A) Origin B) x-axis

C) y-axis D) No symmetry

71) What symmetry does the graph of y = f(x) exhibit? 71)

A) Origin B) y-axis

C) x-axis D) No symmetry

72) Complete the table if f is an even function. 72)

A)

- +

B)

C) D)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers

the question.

73) Complete the right half of the graph of y = f(x) for each of the

following conditions:

(i) f is odd.

(ii) f is even.

73)



Write an equation that results in the indicated translation.

74) The squaring function, shifted 4 units upward 74)

A) y = B)

y = - 4

C) D) y = + 4

y =

75) The absolute value function, shifted 9 units to the right 75)

A) y = 9 B) y =

C) y = D) y = 9

76) The absolute value function, shifted 8 units upward 76)

+ -

- +

A) y = - 8 B) y =

C) y = + 8 D) y =

77) The square root function, shifted 9 units to the right 77)

A) y = + 9 B) y =

C) y = - 9 D) y =

78) The square root function, shifted 7 units to the left 78)

A) y = B) y = + 7

C) y = D) y = - 7

79) The square root function, shifted 2 units upward 79)

A) y = 2 B) y = 2

C) y = D) y =

80) The square root function, shifted 3 units downward 80)

A) y = 3 B) y = 3

C) y = D) y =

Use translations of one of the basic functions to sketch a graph of y = f(x) by hand.

81) y = - 6 81)

A)

B)

y =

C)

D)

82) 82)

A)

B)

C)

D)

83)

y = - 5

A)

B)

C)

D)

83)

y =

84) 84)

A)

B)

C)

y = + 1

D)

85) 85)

A)

B)

y = - 5

C)

D)

86) 86)

A)

B)

C)

D)

87) y = - 5

A)

B)

C)

D)

87)

The function Y2 is defined as Y1 + k for some real number k. Based upon the given

information about Y1 and Y2, find k.

88) 88)

A) 2 B) 4 C) 5 D) 1

89) 89)

A) -4 B) 5 C) -5 D) 4

90) 90)

A) -10 B) -6 C) 10 D) 6

91) 91)

A) -2 B) -1 C) 2 D) 1

92) 92)

A) 28 B) 12 C) -15 D) -25

93) 93)

A) 4 B) 5 C) -2 D) -3

94) 94)

A) -5 B) -1 C) 3 D) 4

95)

A) 9 B) -8 C) 7 D) -6

96) 96)

A) -5 B) 4 C) -4 D) 3

97) 97)

A) 5 B) -4 C) -5 D) 4

Determine the domain and range of the function from the graph.

98) 98)

A) (-∞, 0) ∪ (0, ∞); (-∞, 0) ∪ (0, ∞)

B) (-∞, ∞); [ -8, ∞)

C) (-∞, 0); (-∞, 0)

D) (0, ∞); [ 24, ∞)

95)

99) 99)

A) (-∞, -2]; [0, ∞)

B) , ∞); (-∞, 0]

C) (-∞, ∞); [0, ∞)

D) (-∞, -2) ∪ ( -2, ∞); (-∞, 0) ∪ (0, ∞)

100) 100)

A) [ 4, ∞); [0, ∞) B) [0, ∞); [0, ∞)

C) [ -4, ∞); (-∞, 0] D) [0, ∞); [ 4, ∞)

101) 101)

A) (-∞, ∞); (-∞, ∞) B) [ - 6, ∞); (-∞, ∞)

C) (-∞, ∞); [ - 6, ∞) D) (-∞, ∞); [0, ∞)

102)

_

A) (-∞, ∞); [ -2, ∞) B) (-∞, ∞); (-∞, ∞)

C) [ 4, ∞); (-∞, ∞) D) [0, ∞); [0, ∞)

Use translations of one of the basic functions defined by y = , y = , y = , or y = to

sketch a graph of y = f(x) by hand. Do not use a calculator.

103) y = - 4 103)

A)

B)

102)

C)

D)

104) y = ∣ x - 4∣ 104)

A)

B)

C)

D)

105) y =

_

A)

B)

C)

D)

105)

106) y = + 4 106)

A)

B)

C)

y =

D)

107) 107)

A)

B)

C)

D)

108) y = -4 + ∣ x∣ 108)

A)

B)

C)

D)

109) y = - 3

_

A)

B)

C)

D)

109)

y = - 1

110) 110)

A)

B)

C)

y = - 4

D)

111) 111)

A)

B)

C)

D)

112) y = |x + 7| + 1 112)

A)

B)

C)

D)

113) y = + 2

_

A)

B)

C)

D)

113)

- 3

The graph is a translation of one of the basic functions defined by y = , y = , y = , or y

= . Find the equation that defines the function.

114) 114)

B) y = + 1

D) y =

115) 115)

B) y = + 3

D) y =

116)

A) y =

C) y = - 4

A) y =

C) y =

_

116)

A) y = B) y = + 3

C) y = D) y = - 4

117) 117)

B) y =

D) y = + 2

118) 118)

B) y = - 2

D) y =

119)

A) y =

C) y =

- 5

A) y =

C) y = - 2

_

A) y = -2

B) y = - 4

C) y = 2

D) y = - 4

Find the linear equation that meets the stated criteria.

120) The linear equation y = 246x + 6320 provides an approximation of the

annual cost (in dollars) to rent an apartment at the Leisure Village

Retirement Community, where x = 1 represents 1978, x = 2 represents

1979, and so on. Write an equation that yields the same y-values when

the exact year number is entered.

A) y = 246(x - 1978) + 6320 B) y = 246( 1977 - x) + 6320

C) y = 246(x - 1977) + 6320 D) y = 246( 1978 - x) + 6320

121) The linear equation y = 473x + 3420 provides an approximation of the

annual cost (in dollars) of health insurance for a family of three, where

represents 1984, represents 1985, and so on. Write an

equation that yields the same y-values when the exact year number is

entered.

A) y = 473(x - 1984) + 3420 B) y = 473( 1983 - x) + 3420

C) y = 473( 1984 - x) + 3420 D) y = 473(x - 1983) + 3420

122) The linear equation y = 71.33x + 1019 provides an approximation of

the value (in dollars) of an account opened on January 1, 1989, in the

amount of $ 1019 and earning 7% simple interest, where x = 0 represents

January 1, 1989, x = 1 represents January 1, 1990, x = 2 represents

January 1, 1991, and so on. Write an equation that yields the same

y-values when the exact year number is entered.

A) y = 71.33( 1989 - x) + 1019 B) y = 71.33(x - 1989) +

1019

120)

121)

122)

C) y = 71.33(x - 1990) +

1019

D) y = 71.33( 1990 - x) + 1019

123) The table shows the number of members in the Windy City Edsel squar

Owners Club during the years 1980-1984. Use aes

calcu regres

lator sion

to

find

the

line

for

this

least data,

119)

where x 123)

= 0

_

represent

s 1980, x

= 1

represent

s 1981,

and so

on.

A) y = 8.1x + 59

B) y = 8.3x + 61

C) y = 7.9x + 63 D) y = 8.5x + 62

124) The table shows the number of members in the Windy City Edsel

Owners Club during the years 1986-1990.

Use a calculator to find the least squares regression line for this data,

where x = 0 represents 1986, x = 1 represents 1987, and so on.

A) y = 28.1x + 109 B) y = 28.3x + 106

C) y = 28.4x + 105 D) y = 27.6x + 111


125) Explain how the graph of g(x) = f(x) - 9 is obtained from the graph of y

= f(x).

A) Shift the graph of f to the right 9 units.

B) Shift the graph of f to the left 9 units.

C) Shift the graph of f upward 9 units.

D) Shift the graph of f downward 9 units.

126) Explain how the graph of g(x) = f(x - 3) is obtained from the graph of y

= f(x).

A) Shift the graph of f downward 3 units.

B) Shift the graph of f to the right 3 units.

C) Shift the graph of f to the left 3 units.

D) Shift the graph of f upward 3 units.

127) Which function represents a vertical translation of the parabola

?

A) y = + 5

B) y = + 6

C) y = + 5

D) y = - + 5

128) The graph shown is a translation of the function . The graph

shown is of the form . What are the values of h and k?

124)

125)

126)

127)

_

A) h = -2, k = 2 B) h = 2 k = 2

C) h = -2, k = -2 D) h = 2, k = -2

129) Sketch the graph of y = f(x - 3) for the given graph of y = f(x). 129)

A)

B)

C)

128)

D)

130) Sketch the graph of y = f(x + 2) for the given graph of y = f(x). 130)

A)

B)

C)

D)

131) Use the graph of y = f(x) to find the x-intercepts of the graph of y = f(x +

2).

_

A) 0, 2, 6 B) -3, 0 C) -4, -2, 2 D) -2, 0, 4

131)

1) A

2) A

3) C

4) D

5) C

6) B

7) D

8) C

9) B

10) D

11) D

12) A

13) C

14) B

15) B

16) A

17) D

18) D

19) A

20) B

21) C

22) C

23) D

24) A

25) A

26) A

27) A

28) A

29) A

30) A

31) B

32) B

33) B

34) B

35) A

36) A

37) B

38) C

39) C

40) C

41) C

42) B

43) C

44) C

45) A

46) C

47) B

48) C

49) A

50) A

51) C

52) B

53) B

54) A

55) C

56) C

57) B

58) A

59) A

60) B

61) A

62) B

63) B

64) A

65) C

66) C

67) A

68) C

69) B

70) C

71) A

72) A

73) (i) f is odd.

(ii) f is even.

74) D

75) C

76) C

77) B

78) C

79) A

80) A

81) C

82) D

83) C

84) B

85) A

86) D

87) B

88) B

89) C

90) C

91) A

92) C

93) D

94) A

95) B

96) A

97) D

98) B

99) A

100) D

101) C

102) B

103) B

104) B

105) D

106) D

107) C

108) C

109) A

110) B

111) B

112) D

113) A

114) C

115) A

116) A

117) B

118) B

119) D

120) C

121) D

122) B

123) D

124) A

125) D

126) B

127) B

128) C

129) A

130) D

131) C

7.6

= ; = - 5

=



Write the equation that results in the desired transformation.

1) The square root function, reflected across the x-axis 1)

A) y = - 1 B) y = -

C) y = D) y =

2) The squaring function, vertically stretched by a factor of 9 2)

A) y = B)

y = 9(x -

C) y = D)

y =

3) The cubing function, vertically shrunk by a factor of 0. 7 3)

A) y = B) y =

C) y = 0. 7

D) y 0. 7

4) The squaring function, vertically stretched by a factor of 6 and

reflected across the x-axis

A) y = B) y =

C) y = D)

y = 6(x -

4)

5) The absolute value function, vertically stretched by a factor of 7.6 and

reflected across the x-axis

A) y = - B) y = -7.6

5)

C) y = D) y = 7.6

6) The absolute value function, vertically stretched by a factor of 6.3 and

reflected across the y-axis

A) y = -6.3 B) y =

C) y = 6.3 D) y =

6)

Use transformations of graphs to sketch the graphs of and . Graph as a dashed curve.

7) 7)

A)

B)

C)

D)

8) = ∣ x∣ ; = ∣ x - 6∣

_

A)

B)

C)

D)

8)

= ; =

9) 9)

A)

B)

C)

= ; = -4

D)

10) 10)

A)

B)

= ; = - 2

C)

D)

11) 11)

A)

B)

C)

D)

12) = , = - + 4

A)

B)

C)

D)

12)

= , = + 4

13) 13)

A)

B)

C)

= , = - 6

D)

14) 14)

A)

B)

= , = + 3

C)

D)

15)

15)

A)

B)

C)

D)

Fill in each blank with the appropriate response.

16) The graph of y = can be obtained from the graph of y = by

vertically stretching by a factor of and reflecting across the -axis.

A) 3; y B) -3; y C) -3; x D) 3; x

16)

17) The graph of y = can be obtained from the graph of y = by

vertically stretching by a factor of and reflecting across the -axis.

A) -4; x B) 4; y C) 4; x D) -4; y

18) The graph of y = + 8 can be obtained from the graph of y =

by shifting horizontally units to the , vertically stretching

by a factor of reflecting across the -axis, and shifting vertically

units in the direction.

17)

18)

A) 4; right; 8; y; 5;

downward

B) 4; left; 5; x; 8; upward

C) 4; right; 5; x; 8; upward D) 4; right; 8; x; 5; upward

19) The graph of y = - 7 can be obtained from the graph of y =

by shifting horizontally units to the , vertically stretching



A) 4; right; 5; x; 7; upward B) 4; left; 5; x; 7; downward

C) 4; left; 7; x; 5; downward D) 4; right; 5; x; 7;

downward

19)

20)

The graph of y = - - 8 can be obtained from the graph of y =

by shifting horizontally units to the , vertically shrinking



20)

A)

2; right; ; x; 8;

downward

C)

2; left; ; x; 8; downward

B)

2; right; ; x; 8; upward

D)

2; left; 8; x; ; downward

21) The graph of y = - + 2 can be obtained from the graph of y =

by reflecting across the -axis, vertically shrinking by a factor of

reflecting across the -axis, and shifting vertically units in the

direction.

21)

A)

y; ; x; 2; upward

C)

x; 2; y; ; upward

B)

y; ; x; 2; downward

D)

x; ; x; 2; upward

Give the equation of the function whose graph is described.

22) The graph of y = is vertically stretched by a factor of 7, and the

resulting graph is reflected across the x-axis.

A) y = -7 B) y = -

C) y = 7 D) y =

22)

-7

y = - + 4

y =

23) The graph of y = is shifted 4 units to the right. This graph is then

vertically stretched by a factor of 5 and reflected across the x-axis.

Finally, the graph is shifted 8 units upward.

A) y = -5 + 8

B) y = -5 + 4

C) y = -5 + 8

D) y = -5 - 8

24) The graph of y = is shifted 4 units to the left. This graph is then

vertically stretched by a factor of 5 and reflected across the x-axis.

Finally, the graph is shifted 8 units downward.

A) y = -5 + 8

B) y = -5 - 8

C) y = -5 - 4

D) y = -5 - 8

25) The graph of y = is shifted 3 units to the left. This graph is then

vertically shrunk by a factor of and reflected across the x-axis.

Finally, the graph is shifted 8 units downward.

23)

24)

25)

A)

y = - + 8

C)

y = - - 8

B)

y = - - 8

D)

y = - 8

26) The graph of y = is reflected across the y-axis and vertically shrunk

by a factor of . This graph is then reflected across the x-axis. Finally,

the graph is shifted 4 units upward.

26)

A) B)

C) D)

y = - + 4

y = + 4

27) The graph of y = is shifted 5.4 units to the right and then vertically

shrunk by a factor of 0. 8.

A) y = 0. 8

B) y = 0. 8

C) y = 5.4

D) y = 0. 8 + 5.4

28) The graph of y = is vertically stretched by a factor of 2. This graph

is then reflected across the x-axis. Finally, the graph is shifted 0.33

units downward.

A) y = 2 B) y = 2 - 0.33

C) y = 2 - 0.33 D) y = -2 - 0.33

29) The graph of y = is reflected across the y-axis. This graph is then

vertically stretched by a factor of 6.0. Finally, the graph is shifted 5

units downward.

A) y = - 5 B) y = - 5

27)

28)

29)

f(x) =

A) g(x) = - 3

C) g(x) = -3

C) y = 6.0 + 5 D) y = 5 - 6.0

30) The graph of y = is shifted 5.4 units to the left. This graph is then

vertically stretched by a factor of 5.0. Finally, the graph is reflected

across the x-axis.

30)

A) y = 5.0

C) y = -5.4

B) y = -5.0

D) y = -5.0

The graph of the given function is drawn with a solid line. The graph of a function, g(x),

transformed from this one is drawn with a dashed line. Find a formula for g(x).

31) 31)

B) g(x) =

D) g(x) =

32) f(x) = 32)

33)

f(x) =

B) g(x) = 6

D) g(x) = -6

A) g(x) =

C) g(x) =

- 3

- 3

f(x) =

A)

g(x) = - + 3

C)

g(x) = - 3

B) g(x) = + 3

D)

g(x) = -

34) 34)

A) g(x) = 4 + 0.25 B) g(x) = 4 - 0.25

C) g(x) = 0.25 - 4 D) g(x) = 0.25 + 4

Use transformations to graph the function.

35)

35)

A)

33)

f(x) = -4

B)

C)

D)

36) f(x) = - 5

A)

B)

C)

D)

36)

f(x) =

37) 37)

A)

B)

C)

f(x) = 7 - 7

D)

38) 38)

A)

B)

f(x) = - 7

C)

D)

39) 39)

A)

B)

C)

D)

40) f(x) = - 6

A)

B)

C)

D)

40)

f(x) = - + 1

41) 41)

A)

B)

C)

D)

42) f(x) = - 6 42)

A)

B)

C)

D)

43)

f(x) = - + 5

A)

B)

C)

D)

43)

Use the accompanying graph of y = f(x) to sketch the graph of the indicated function.

44) y = -f(x) 44)

A)

B)

C)

D)

45) y = f(-x) 45)

A)

B)

C)

D)

46) y = f(-x) 46)

A)

B)

C)

D)

47) y = -f(x)

A)

B)

C)

47)

D)

48) y = 2f(x) 48)

A)

B)

C)

D)

49)

y = - f(x)

A)

49)

B)

C)

D)

50) y = - f(2x)

A)

B)

C)

50)

D)

51) y = f(x - 3) 51)

A)

B)

C)

D)

52)

y = - f(x + 4) + 5

52)

A)

B)

C)

D)

Let f be a function with the given domain and range. Find the domain and range of the

indicated function.

53) Domain of f(x): [ 5, 10]; Range of f(x): [0, 4]

-f(x)

A) D: [ 5, 10]; R: [0, 4] B) D: [ 5, 10]; R: [-4, 0]

C) D: [ -10, -5]; R: [-4, 0] D) D: [ -10, -5]; R: [0, 4]

54) Domain of f(x): [ 2, 7]; Range of f(x): [0, 4] f(-

x)

A) D: [ 2, 7]; R: [-4, 0] B) D: [ -7, -2]; R: [-4, 0]

C) D: [ 2, 7]; R: [0, 4] D) D: [ -7, -2]; R: [0, 4]

55) Domain of f(x): [ 3, 5]; Range of f(x): [0, 5]

f(x - 2)

A) D: [ 5, 7]; R: [0, 5] B) D: [ 1, 6]; R: [0, 5]

C) D: [ 3, 5]; R: [-2, 3] D) D: [ 3, 8]; R: [ 2, 7]

56) Domain of f(x): [-3, 4]; Range of f(x): [0, 2]

f(x + 4) + 2

A) D: [ 1, 8]; R: [ 2, 4] B) D: [ 1, 8]; R: [-2, 0]

C) D: [ -7, 0]; R: [ 2, 4] D) D: [ -7, 0]; R: [-2, 0]

57) Domain of f(x): [-4, 5]; Range of f(x): [0, 2]

3f(x + 6)

A) D: [ -10, -1]; R: [0, 6] B) D: [ 2, 11]; R: [ 3, 5]

C) D: [ 2, 11]; R: [0, 6] D) D: [ -10, -1]; R: [ 3, 5]

58) Domain of f(x): [-3, 0]; Range of f(x): [0, 7] f(-

2x)

53)

54)

55)

56)

57)

58)

A)

D: ; R: [0, 7]

B) D: [-3, 0]; R: [-14, 0]

C) D: [0, 6]; R: [0, 7] D)

D: [-3, 0];

59) Domain of f(x): [-3, 0]; Range of f(x): [0, 4] 59)

3f

A)

D: ; R: [0, 12]

B) D: [-15, 0]; R: [0, 12]

C) D: [-9, 0]; R: [0, 20] D)

D: ; R:

Determine the intervals on which the function is increasing, decreasing, and constant.

60)

60)

A) Increasing on (-∞, -1]; Decreasing on [-1, ∞)




61) 61)


B) Increasing on (-∞, 0]; Decreasing on [0, ∞)

C) Increasing on (∞, 0]; Decreasing on [0, -∞)


62) 62)




D) Increasing on (∞, 0]; Decreasing on [0, -∞)

63) 63)



C) Increasing on [3, ∞); Decreasing on [ 3, ∞)

D) Increasing on (-∞, 3]; Decreasing on [ 3, ∞)

64) 64)

A) Increasing on [0, ∞); Decreasing on (-∞, 0]

B) Increasing on (-∞, ∞)

C) Decreasing on (-∞, ∞)


65) 65)

A) Increasing on [ 4, ∞); Decreasing on [ -4, ∞); Constant on [ -4, 4]

B) Increasing on (-∞, 4]; Decreasing on [ -4, ∞); Constant on [4, ∞)

C) Increasing on (-∞, 4]; Decreasing on (-∞, -4]; Constant on [4, ∞)

D) Increasing on [ 4, ∞); Decreasing on (-∞, -4]; Constant on [ -4, 4]

66) 66)

A) Increasing on [-2, 0] and [3, 5]; Decreasing on [1, 3]; Constant on

B) Increasing on [-2, 0] and [3, 4]; Decreasing on [-5, -2] and [1, 3]

C) Increasing on [1, 3]; Decreasing on [-2, 0] and [3, 5]; Constant on

[2, 5] D) Increasing on [-1, 0] and [3, 5]; Decreasing on [0, 3]; Constant on

[-5, -3]

67) 67)

A) Increasing on [-3, 1]; Decreasing on [-5, -3] and [0, 5]; Constant on

[1, 2]

B) Increasing on [-3, -1]; Decreasing on [-5, -2] and [2, 4]; Constant on

[-1, 2]

C) Increasing on [-5, -3] and [2, 5]; Decreasing on [-3, 0]; Constant on

[0, 2]

D) Increasing on [-3, 0]; Decreasing on [-5, -3) and [2, 5]; Constant on

[0, 2]

Shown here are graphs of y1 and y2. The point whose coordinates are given at the bottom of

the screen lies on the graph of y1. Use this graph, and not your own calculator, to find the

value of y2 for the same value of x shown.

68) 68)

A) 2 B) -8 C) -2 D) -32

69) 69)

A) -2.3333333 B) 21

C) 2.3333333 D) 27

70) 70)

A) 14.797273 B) -7.3986363

C) 7.3986363 D) 0.8220707

71) 71)

A) -6 B) -1.5 C) -9 D) 6

72) 72)

A) 27 B) 0.6666666

C) -6 D) 6

73) 73)

A) 0.4199736 B) -16

C) 15.119053 D) -15.119053

The figure shows a transformation of the graph of y = . Write the equation for the graph.

74)

74)

- 3

A) g(x) = B)

g(x) = + 3

C) g(x) = D) g(x) =

75) 75)

A) g(x) = -x2 + 1 B) g(x) = -(x - 1)2

C) g(x) = (x + 1)2 D) g(x) = -x2 - 1

76) 76)

A) g(x) = (-x + 1)2 B) g(x) = (-x - 1)2

C) g(x) = -x2 - 1 D) g(x) = -x2 + 1

77)

A)

A)

g(x) = x2 - 4

B)

g(x) = x2 + 4

C) g(x) = (x - 4)2 D)

g(x) = (x + 4)2

78) 78)

g(x) = (x + 2)2

B)

g(x) = (x - 2)2

C)

g(x) = (x2 - 2)

D) g(x) = -x2 + 2

79) 79)

A) g(x) = -x2 - 6 B) g(x) = -x2 + 6

C) g(x) = -(x + 6)2 D) g(x) =


77)

80) True or false? If r is an x-intercept of the graph of y = f(x), then

has an x-intercept at x = r.

A) True B) False

81) True or false? If b is a y-intercept of the graph of y = f(x), then

has a y-intercept at x = -b.

A) True B) False

82) True or false? If the function y = f(x) increases on the interval (a, b) of

its domain, then y = -f(x) increases on the interval (a, b).

A) True B) False

83) If b is a y-intercept of the graph of y = f(x), then y = 3f(x) has a

of which of these points?

A) 3b B) -3b C) -b D) b

84) True or false? If the function y = f(x) increases on the interval (a, b) of

its domain, and we are given that c < 0, then the graph of

decreases on the interval

A) False B) True

85) True or False. If the graph of y = f(x) is symmetric with respect to the

then the graph of y = -f(x) is symmetric with respect to the

80)

81)

82)

83)

84)

85)

y-a xis.

A) False B) True

86) True or False. If the graph of y = f(x) is symmetric with respect to the

origin, then the graph of y = -f(x) is symmetric with respect to the

origin.

A) False B) True

86)

1) B

2) A

3) C

4) C

5) B

6) C

7) D

8) C

9) D

10) A

11) C

12) D

13) D

14) A

15) A

16) D

17) C

18) C

19) B

20) C

21) A

22) A

23) C

24) D

25) C

26) B

27) A

28) D

29) B

30) B

31) C

32) C

33) A

34) C

35) D

36) A

37) B

38) A

39) D

40) B

41) A

42) D

43) C

44) B

45) B

46) B

47) D

48) D

49) C

50) C

51) A

52) B

53) B

54) D

55) A

56) C

57) A

58) A

59) B

60) B

61) D

62) C

63) D

64) B

65) D

66) A

67) D

68) B

69) B

70) C

71) A

72) D

73) C

74) D

75) B

76) A

77) D

78) C

79) C

80) A

81) A

82) B

83) A

84) B

85) B

86) B



The graph of the function y = f(x) is given below. Sketch the graph of y = .

1) 1)

A)

B)

C)

D)

2) 2)

A)

B)

C)

D)

3) 3)

A)

B)

C)

D)

4) 4)

A)

B)

C)

D)

5)

_

A)

B)

C)

D)

5)

6) 6)

A)

B)

C)

D)

7) 7)

A)

B)

C)

D)

8) 8)

A)

B)

C)

D)

9)

_

A)

B)

C)

D)

9)

10) 10)

A)

B)

C)

D)


11) If the range of y = f(x) is (-∞, ∞), what is the range of y = ? 11)

A) [0, ∞) B) (-∞, ∞) C) (-∞, 0] D) (0, ∞)

12) If the range of y = f(x) is (-∞, 0], what is the range of y = ? 12)

A) (-∞, ∞) B) [0, ∞) C) (0, ∞) D) (-∞, 0]

13) If the range of y = f(x) is [ 8. 6, ∞), what is the range of y = ? 13)

A) [0, ∞) B) (-∞, ∞) C) [ 8. 6, ∞) D) (-∞, 8.

6]

14) If the range of y = f(x) is [ -12. 4, ∞), what is the range of y = ? 14)

A) (-∞, 0] B) (-∞, -12. 4]

C) [ 12. 4, ∞) D) [0, ∞)

15) If the range of y = f(x) is (-∞,

A) (-∞, ∞)

13. 7), what is the range of y =

B) (-∞, -13. 7]

? 15)

C) [ 13. 7, ∞) D) [0, ∞)

16) If the range of y = f(x) is (-∞, -12. 2], what is the range of y = ? 16)

A) (-∞, 12.

2]

B) [ 12. 2,

∞)

C) [0, ∞) D) [ -12. 2,

∞)

Use the graph, along with the indicated points, to give the solution set of the equation or

inequality.

17) y1 > y2

A) (-∞, 0) ∪ (4, ∞) B) (0, 4)

C) [0, 4] D) (-∞, 0] ∪ [4, ∞)

18) y1 = y2 18)

A) {1, 5} B) [1, 5] C) (1, 5) D) {-4}

19) y1 = y2

17)

19)

A) (-5, 3) B) {3} C) (-∞, -5] D) {-5}

20) y1 = y2 20)

A) {-2} B) (-∞, ∞) C) {2} D) ∅

21) y1 = y2 21)

A) (-2, 0) B) {0} C) (-∞, ∞) D) ∅

22) y1 ≥ y2 22)

A) (-1, 5) B) [-1, 5]

C) (-∞, 1) ∪ (5, ∞) D) (-∞, -1] ∪ [5, ∞)

Solve the equation.

23) = 0 23)

A) { -6} B) { 6, -6} C) (-∞, -6) D) ( 6,∞)

24) = 5 24)

+ 7 =

A)

C)

- 4 = 2

A)

C)

A) B)

C) D)

25)

B)

D)

26) = 9 26)

A) { 9.4, 8.6} B) { 9.4, -8.6}

C) { -9.4} D) ∅

27) + 2 = 6 27)

A) { -1, -9} B) { -1} C) { 1, 9} D) ∅

28) 15 28)

B)

D) ∅

29) 29)

B)

D) ∅

30) + 9 = 5 30)

A) B)

C) D) ∅

31) 3 - 3 =

A)

C)

3 B)

D)

31)

32) +

A) { - 4, 3}

2 = 9

B)

C)

D) ∅

32)

Solve the inequality.

33) > 5 33)

A) ( -1, ∞) B) (-11, -1)

C) (-∞, -11) ∪ ( -1, ∞) D) ∅

34) > 8 34)

25) = 16

A)

C)

+ 6 <

A)

C)

=

A)

A) B)

∪

C) D)

∪

35)

∪

35)

B)

∪

D)

36) ≤ 11 36)

A) B)

(-∞, 3] ∪

C) D)

(-∞, -3] ∪

37) ≤ 7 37)

A) [ -1, 13] B) [ -1, ∞)

C) (-∞, -1] ∪ [ 13, ∞) D) [ 13, ∞)

38) 9 38)

B)

D) ∅

∪

39) - 6 > 8 39)

A) ( -5, 23) B) (-∞, -5) ∪ ( 11, ∞)

C) (-∞, -5) ∪ ( 23, ∞) D) (-∞, -11) ∪ ( 5, ∞)

B) (-∞, ∞) C) D) ∅

40)

41) ≤ 0 41)

A) { 7} B) (-∞, 7) C) { -7} D) ∅

42) < 0 42)

A) { 4} B) (-∞, 4) C) { -4} D) ∅

Solve the equation.

43)

B)

43)

D)

44) 44)

B)

> 8

A)

C)

40) > -9

A)

=

A)

C)

=

A)

C)

=

A)

C)

=

A)

C)

=

A)

C)

=

A)

C)

C) D)

45) 45)

B)

D)

46) 46)

B)

D)

47) 47)

B)

D) ∅

-

48) 48)

B)

D) ∅

49) 49)

B)

D) ∅

50)

=

A) {16, 0} B) {10, 10} C) {16, 12} D) ∅

50)

51) B) C) D) ∅

51)

Solve the inequality graphically.

52) > 52)

A) (-∞, -5) ∪ (-2, ∞) B) (2, 5)

C) (-5, -2) D) ∅

53) < 53)

A) (2, 5) B) (-∞, -5) ∪ (-2, ∞)

C) (-5, -2) D) ∅

=

A)

54)

55)

>

A) (16, ∞) B) (-∞, 16)

C) (0, 16) D) (-∞, 0) ∪ (16, ∞)

<

A) (16, ∞) B) (-∞, 0) ∪ (16, ∞)

C) (-∞, 16) D) (0, 16)

54)

55)

Solve the equation or inequality graphically. Express solutions or endpoints of intervals

rounded to the nearest hundredth, if necessary.

56) = 56)

A) { -2.37, -1.32} B) { 2.37, 2.37}

C) { 2.37, 1.32} D) { -2.37, 1.32}

57) = 6x - 2 57)

A) { -0.78} B) { 0.78} C) ∅ D) { 1}

58) ≥ -x - 5 58)

A) [ 1.33, 14] B) (-∞, -14] ∪ [ -1.33, ∞)

C) [ -1.33, -14] D) (-∞, 1.33] ∪ [ 14, ∞)

59) > . 4x - 5 59)

A) (-∞, -1] ∪ [ 1.25, ∞) B) ∅

C) [ -1, 1.25] D) (-∞, ∞)

60) < - 60)

A) (-∞, 2.67] ∪ [ 0.5, ∞) B) ∅

C) [ 2.67, 0.5] D) (-∞, ∞)

61) + ≤ -x -

(Provide exact answer.)

A) (-∞, - ] ∪ [ , ∞) B) (-∞, ∞)

C) (-∞, - ] ∪ [ , ∞) D) ∅

61)

62) + = 12 62)

A) { 3, 9} B) {-3, 9} C) {-3} D) ∅

63) + = 16 63)

A) { 11} B) { 11, -5} C) { -11, 5} D) ∅

Solve the problem.

64) The formula to find Fahrenheit temperature, F, given Celsius 64)

temperature, C, is . Find the range, in Fahrenheit, when the

temperature in Celsius is between 3°C and 10°C, inclusive. Round to

the nearest tenth.

A) 33.7°F ≤ Temperature ≤

50°F

B) 5.4°F ≤ Temperature ≤

18°F

B)

D)

> 36

C) 37.4°F ≤ Temperature ≤

50°F

D) 21.4°F ≤ Temperature ≤

34°F

65) The formula to find Celsius temperature, C, given Fahrenheit

temperature, F, is If the processing temperature of a

chemical ranges from to inclusive, then what is the range

of its temperature in degrees Celsius?

A) 270°C ≤ Temperature ≤ 315°C

B) 150°C ≤ Temperature ≤ 175°C

C) 100°C ≤ Temperature ≤ 175°C

D) 32°C ≤ Temperature ≤ 45°C

66) The temperature on the surface of the planet Krypton in degrees Celsius

satisfies the inequality ≤ 53. What range of temperatures

corresponds to this inequality? (Use interval notation.)

A) [ 1, 107] B) [ -107, 1]

C) [ -107, -1] D) [ -1, 107]

67) Dr. Hughes found that the weight, w, of 99% of her students at

Cantanople University satisfied the inequality < 58. What

range of weights corresponds to this inequality? (Use interval notation.)

A) (-∞, 102] ∪ [ 218, ∞) B) (-∞, 102) ∪ ( 218, ∞)

C) ( 102, 218) D) [ 102, 218]

68) The Fahrenheit temperature, F, in Siber City in October ranges from

Write an absolute value inequality whose solution is this

65)

66)

67)

68)

range.

A) < 17

C) < 70

< 53

69) In a milling operation, the thickness of the metal bars that can be

produced satisfies the inequality What range of

thicknesses corresponds to this inequality?

A) [ 0.38, 3.03] B) [ 1.14, 1.89]

C) [ 0.75, 3.03] D) [ 0.75, 6.06]

70) The average annual growth rate of Palmetto palms in inches satisfies

the inequality What range of growth corresponds to

this inequality?

A) [ 0.7, 12.28] B) [ 2.72, 3.42]

C) [ 0.35, 6.14] D) [ 0.7, 6.14]

71) The number of non-text books read by college students ranges from 5

to 61. Using B as the variable, write an absolute value inequality that

corresponds to this range.

A) ≤ 33 B) ≤ 28

C) ≤ 5 D) ≤ 56

69)

70)

71)

72) A real estate development consists of home sites that range in width fro m 45

to 97

feet and

in depth

from

135 to

195 feet.

Using x

as the

variable

in both

cases,

write

absolute

value

inequaliti

es that

correspo

nd to

these

ranges.

72)

A) ≤ 52, ≤ B) ≤ 26, ≤

60 30

C) ≤ 71, ≤ D) ≤ 45, ≤

165 135

73) The inequality ≤ 15 describes the range of monthly average

temperatures T in degrees Fahrenheit at a City X. (i) Solve the

inequality. (ii) If the high and low monthly average temperatures satisfy

equality, interpret the inequality.

A) 14 ≤ T; The monthly averages are always greater than or equal to

B) T ≤ 55; The monthly averages are always less than or equal to

C) 14 ≤ T ≤ 66; The monthly averages are always within

D) 25 ≤ T ≤ 55; The monthly averages are always within

73)


74) True or false? The graph of y = is the same as that of y = f(x) for

values of f(x) that are nonnegative; and for values of y = f(x) that are

negative, the graph is reflected across the

A) True B) False

75) One of the graphs below is that of y = f(x), and the other is that of

. State which is the graph of y = .

74)

i

75)

A) i B) ii

76) One of the graphs below is that of y = f(x) and the other is that of

State which is the graph of y = .

76)

A) i B) ii

77) Given a = 7, b = -16, which of the following statements is false?

77)

A) = -ab

B) + ≥ -(a+b)

C) = a/b

78) Given a = -1, b = -8, which of the following statements is false?

A) = -ab

B) + = -(a+b)

C) = a/b

78)

79) The graph shown is a translation of the function of the form 79)

. What are the values of h and k?

A) h = -3, k = 2 B) h = -3, k = -2

C) h = 3, k = 2 D) h = 3, k = -2

80) Use graphing to determine the domain and range of y = for f(x) =

- - 2.

A) D: (-∞, ∞); R: [-2, ∞) B) D: [0, ∞); R: (-∞, 2]

C) D: (-∞, ∞); R: [ 2, ∞) D) D: [0, ∞); R: (-∞, -2]

81) Use graphing to determine the domain and range of y = for f(x) =

- 5.

80)

81)

A) D: [0, ∞); R: [-5, ∞) B) D: (-∞, ∞); R: [0, ∞)

C) D: [0, ∞); R: (-∞, ∞) D) D: (-∞, ∞); R: [ 5, ∞)

Find the requested value.

82)

f(x) =

A) -42 B) -10 C) 2 D) 42

83)

f(0) for f(x) =

A) 4 B) 7 C) -6 D) -9

84)

f( 6) for f(x) =

A) -24 B) 43 C) 6 D) 5

85)

f( 7) for f(x) =

A) 7 B) -7 C) 25 D) 49

86)

f( -3) for f(x) =

A) -14 B) 24 C) -9 D) 16

Graph the function.

87)

f(x) =

A)

82)

83)

84)

85)

86)

87)

B)

C)

D)

88)

f(x) =

A)

B)

C)

D)

88)

89)

f(x) =

A)

B)

89)

C)

D)

90)

f(x) =

90)

A)

B)

C)

D)

91)

f(x) =

A)

B)

C)

D)

91)

92) 92)

A)

B)

C)

D)

Use a graphing calculator to graph the piecewise-defined function, using the window

indicated.

93) f(x) = ; window [-4, 6] by [-2, 8]

A)

B)

93)

C)

D)

94)

f(x) = ; window [-2, 5] by [-1, 6]

A)

B)

94)

C)

D)

95)

f(x) = window [-10, 6] by [-6, 10]

A)

B)

95)

C)

D)

96)

f(x) = ; window [-4, 4] by [-4, 4]

A)

B)

96)

C)

D)

97) 97)

A)

B)

C)

D)

98) 98)

A)

B)

C)

D)

99)

f(x) = ; window [-10, 5] by [-10, 10]

A)

B)

99)

C)

D)

100)

f(x) = ; window [-5, 5] by [-10, 2]

A)

B)

100)

C)

D)

101)

f(x) = ; window [-5, 5] by [-10, 10]

A)

B)

101)

C)

D)

102)

f(x) = ; window [-6, 5] by [-10, 6]

A)

B)

102)

C)

D)

Give a formula for a piecewise-defined function f for the graph shown.

103) 103)

A) B)

f(x) =

C)

f(x) =

f(x) =

D)

f(x) =

104)

_

A) B)

f(x) =

C)

f(x) =

f(x) =

D)

f(x) =

105) 105)

A) B)

f(x) =

C)

f(x) =

f(x) =

D)

f(x) =

106) 106)

A) f(x

104)

) = B)

C)

f(x) =

f(x

) =

D)

f(x) =

107) 107)

A) B)

f(x) =

C)

f(x) =

f(x) =

D)

f(x) =

108) 108)

A) B)

f(x) =

C)

f(x) =

f(x) =

D)

f(x) =

109)

109)

A)

f(x) =

B)

f(x) =

C)

f(x) =

D)

f(x) =

110) 110)

A)

f(x) =

B)

f(x) =

C)

f(x) =

D)

f(x) =

111)

_

111)

A) f(x) = - 5

B)

f(x) =

C)

f(x) =

D)

f(x) =

112) 112)

A) B)

f(x) =

C)

f(x) =

f(x) =

D)

f(x) =

Graph the equation.

113) y = + 1

_

A)

B)

C)

D)

113)

y =

114) 114)

A)

B)

C)

y = - 1

D)

115) 115)

A)

B)

y =

C)

D)

116) 116)

A)

B)

C)

D)

117) y =

_

A)

B)

C)

D)

117)

Solve the problem.

118) A video rental company charges $ 4 per day for renting a video tape,

and then $ 3 per day after the first. Use the greatest integer function

and write an expression for renting a video tape for x days.

A) y = 3 + 4 B) y =

C) y + 4 = 3 D) y = 3x + 4

119) Suppose a car rental company charges $ 74 for the first day and $ 24 for

each additional or partial day. Let S(x) represent the cost of renting a

car for x days. Find the value of S( 5.5).

A) $ 194 B) $ 206 C) $ 132 D) $ 182

120) Suppose a life insurance policy costs $ 12 for the first unit of coverage

and then $ 3 for each additional unit of coverage. Let C(x) be the cost

for insurance of x units of coverage. What will 10 units of coverage

cost?

A) $ 30 B) $ 39 C) $ 18 D) $ 42

121) A salesperson gets a commission of $ 400 for the first $10,000 of sales,

and then $ 200 for each additional $10,000 or partial of sales. Let S(x)

represent the commission on x dollars of sales. Find the value of

A) $ 2200 B) $ 1900 C) $ 2100 D) $ 2300

122) Assume it costs 25 cents to mail a letter weighing one ounce or less, and

then 20 cents for each additional ounce or fraction of an ounce. Let L(x)

be the cost of mailing a letter weighing x ounces. Graph y = L(x).

A)

118)

119)

120)

121)

122)

B)

C)

D)

123) Sketch a graph that depicts the amount of water in a 50-gallon tank

during the course of the described pumping operations. The tank is

initially full, and then a pump is used to take water out of the tank at a

rate of 6 gallons per minute. The pump is turned off after 5 minutes.

At that point, the pump is changed to one that will pump water into the

tank. The change takes 2 minutes and the water level is unchanged

during the switch. Then, water is pumped into the tank at a rate of 3

gallons per minute for 3 minutes.

A)

123)

B)

C)

D)

124) The charges for renting a moving van are $60 for the first 20 miles and

$8 for each additional mile. Assume that a fraction of a mile is rounded

up. (i) Determine the cost of driving the van 80 miles. (ii) Find a

symbolic representation for a function f that computes the cost of

driving the van x miles, where (Hint: express f as a

piecewise-constant function.)

A) $540;

f(x) =

B) $860;

f(x) =

C) $540;

f(x) =

D) $5280;

f(x) =

124)

125) Sketch a graph showing the mileage that a person is from home after x

hours if that individual drives at 32.5 mph to a lake 65 miles away,

stays at the lake 1.5 hours, and then returns home at a speed of 65

mph.

A)

125)

B)

C)

126) In Country X, the average hourly wage in dollars from 1945 to 1995 can

be modeled by

the

Use f avera

to ge

estimhourl

f(x) = ate y

wages in 126)

1950, _

1970, and

1990.

A) $ 0.72, $ 3.07, $ 6.71 B) $ 3.45, $ 6.71, $ 2.22

C) $ 3.45, $ 0.34, $ 6.71 D) $ 0.72, $ 2.22, $ 6.71


127) Which of the following is a vertical translation of the function 127)

A) y = [[x]] - 5 B) y = 5[[x]]

C) y = -[[x]] D) y = [[x - 5]]

128) Which of the following is a horizontal translation of the function 128)

A) y = [[x - 3]] B) y = 3[[x]]

C) y = [[x]] - 3 D) y = -[[x]]

129) Which of the following is a reflection of the function y = [[x]] about the

y-axis? Use your graphics calculator to verify your result.

A) y = [[-x]] B) y = -[[x]]

C) y = [[-x + 1]] D) y = -[[x + 1]]

129)

1) B

2) D

3) B

4) C

5) D

6) A

7) A

8) B

9) A

10) B

11) A

12) B

13) C

14) D

15) D

16) B

17) A

18) A

19) D

20) C

21) D

22) D

23) A

24) C

25) B

26) B

27) A

28) C

29) B

30) D

31) C

32) A

33) C

34) B

35) C

36) C

37) A

38) A

39) C

40) B

41) A

42) D

43) A

44) C

45) B

46) B

47) B

48) C

49) C

50) A

51) B

52) A

53) C

54) C

55) B

56) C

57) B

58) A

59) D

60) B

61) D

62) B

63) B

64) C

65) B

66) C

67) C

68) A

69) C

70) D

71) B

72) B

73) D

74) A

75) A

76) B

77) C

78) A

79) D

80) C

81) B

82) A

83) D

84) C

85) D

86) A

87) D

88) D

89) B

90) B

91) C

92) A

93) C

94) A

95) A

96) A

97) A

98) D

99) A

100) A

101) B

102) C

103) D

104) D

105) A

106) B

107) C

108) A

109) C

110) A

111) D

112) D

113) A

114) D

115) C

116) C

117) A

118) A

119) A

120) B

121) A

122) A

123) C

124) C

125) B

126) A

127) A

128) A

129) A

(x).



Find the requested composition or operation.

1) f(x) = 6 - 9x, g(x) =

Find (f + g)(x).

A) -7x + 15

-2x + 9

B) -2x

+ 6

1)

C) -11x + 15 D) 4x

2) f(x) = 8x - 2, g(x) =

Find (f - g)(x).

A) 4x - 5

4x

B) 4x

- 3

+ 1

C) -4x

- 1

D) 12x

- 5

2)

3) f(x) = , g(x) =

Find (fg)(x).

A) ( 2x + 3)( 25x - 16) B) ( 5x - 4

C) ( 2x + 3)( 5x - 4) D)

3)

4) f(x) = 4x - 2, g(x) = 7x + 5

Find (fg)(x).

A) + 6x + 3

B) + 6x - 10

C) - 10

D) - 9x - 10

5) f(x) = - 7x, g(x) = - 3x - 28

Find

A) B)

C) D)

6) f(x) = 3x + 13, g(x) = 4x - 1

Find (f ∘ g)(x).

4)

5)

6)

A) 12x +

51

B) 12x +

12

C) 12x +

10

D) 12x +

16

7) f(x) = , g(x) = 8x - 11

Find (f ∘ g)(x).

A) 2 B) 2

C) 8 D) 8 - 11

8)

f(x) = + 2x + 8, g(x) = 2x - 5

Find (g ∘ f)(x).

A) + 4x + 11

B) + 4x + 21

C) + 2x + 3

D) + 4x + 11

7)

8)

9)

f(x) = , g(x) =

Fi (f ∘ g)(x).

nd

)(

)(

)

)

9)

A) B) C) D)

10)

f(x) = , g(x) = 7x + 3

Find (g ∘ f)(x).

A) x B) x + 6 C) 7x + 18 D)

x -

10)

Perform the requested composition or operation.

11) Find (f + g)( -5) when f(x) = x + 2 and g(x) = x - 1. 11)

A) -9 B) -7 C) -11 D) -13

12) Find (f - g)( -4) when f(x) = -3x2

A) 45 B) -36

+ 7 and g(x) = x

C) -38

+ 1. D) -46

12)

13) Find (fg)( -2) when f(x) = x

A) -115 B) 75

+ 3 and g(x) = 4

C) -27

+ 19x + 7.

D) -15

13)

14)

Find ( -5) when f(x) = 4x - 5 and g(x) = 4 + 14x + 4.

14)

A) 0 B) C) D)

-

15) Find (f ∘ g)( 8) when f(x) = -4x - 5 and g(x) = -4x2 + 5x + 3. 15)

A) -5658 B) -34 C) -49 D) 847

16) Find (g ∘ f)( 4) when f(x) = 9x - 6 and g(x) = -8x2 - 2x + 9. 16)

A) -1149 B) -291 C) -285 D) -7251

Find the specified domain.

17) For f(x) = 2x - 5 and g(x) = , what is the domain of (f + g)? 17)

A) [ 2, ∞) B) [ -2, ∞) C) [0, ∞) D) ( -2, 2)

18)

For f(x) = 2x - 5 and g(x) = , what is the domain of ?

A) ( -9, ∞) B) [0, ∞) C) ( -9, 9) D) [ 9, ∞)

18)

19) For f(x) = 2x - 5 and g(x) = , what is the domain of (f ∘ g)? 19)

A) [0, ∞) B) [ 6, ∞) C) ( -6, 6) D) [ -6, ∞)

20) For f(x) = 2x - 5 and g(x) = , what is the domain of (g ∘ f)? 20)

A) [∞, 1.5) B) [ 2, ∞) C) ( -2, 2) D) [ 1.5, ∞)

21) For f(x) = - 1 and g(x) = 2x + 3, what is the domain of (f - g)? 21)

A) [0, ∞) B) [ 1, ∞) C) ( -1, 1) D) (-∞, ∞)

22) For f(x) =

- 25

and g(x)

= 2x + 3,

what is

the

domain

of ?

22)

A) (-∞, ∞) B)

C) D) ( -5, 5)

∪

23)

For f(x) = - 49 and g(x) = 2x + 3, what is the domain of ?

23)

A) B)

∪

C) (-∞, -7) ∪ ( -7, 7) ∪ ( 7, ∞) D) (-∞, ∞)

24) For f(x) = - 36 and g(x) = 2x + 3, what is the domain of (f ∘ g)? 24)

A) [0, ∞) B) ( -6, 6) C) [ 6, ∞) D) (-∞, ∞)

25)

26)

For f(x) = and g(x) = , what is the domain of (f ∙ g)?

A) [0, 5) ∪ (5, ∞) B) [ 3, 5) ∪ (5, ∞)

C) [ 3, ∞) D) ( 3, 5) ∪ (5, ∞)

For g(x) = and h(x) = , what is the domain of (h ∘ g)?

A) [ -4, 60) ∪ (60, ∞) B) [0, 60) ∪ (60, ∞)

C) [ -4, 8) ∪ ( 8, ∞) D) [0, 8) ∪ ( 8, ∞)

25)

26)

Use the graphs to evaluate the expression.

27) f( -1) + g( -4)

y = f(x) y = g(x)

27)

A) -3 B) 0 C) -5 D) -2

28) f( -2) - g( -4)

y = f(x) y = g(x)

28)

A) -7 B) -1 C) -5 D) -4

29) f( 3) - g( 2)

y = f(x) y = g(x)

C) 5 D) -3

30) f( 4) * g( -4)

y = f(x) y = g(x)

29)

A) B) 4

A) -2 B) C) 8 D) 6

31) (g ∘ f)( -3)

y = f(x) y = g(x)

31)

30)

A) -2.5 B) -1 C) 0.5 D) 1.5

32) (f ∘ g)( -2)

y = f(x) y = g(x)

32)

A) -1.5 B) 1 C) 0 D) -2

33) (f ∘ g)( 0)

y = f(x) y = g(x)

33)

A) 1 B) -1 C) -2 D) -3

34) (g ∘ f)( -1)

y = f(x) y = g(x)

34)

A) -1 B) -2 C) -3 D) -4

35) (f + g)( 3)

y = f(x) y = g(x)

A) -3 B) 4

35)

36) g(f( 4))

y = f(x) y = g(x)

C) 5 D)

A) 6 B) 8 C) -2 D) 4

Use the tables to evaluate the expression if possible.

37) Find (f + g)( -2). 37)

A) 7 B) -2 C) 12 D) -8

38) Find (fg)( -5). 38)

A) 25 B) 3 C) 5 D) 30

39) Find (g ∘ f)( 11). 39)

A) 107 B) 38 C) 67 D) 89

40) Find (f ∘ g)( 3). 40)

36)

A) 14 B) 5 C) 10 D) 3

41) Find (g ∘ f)( 10). 41)

A) 19 B) 21 C) 10 D) 55

42) Find (f ∘ f)( 8). 42)

A) 8 B) 43 C) 21 D) 17

43) Find (g ∘ g)( 3). 43)

A) 15 B) 13 C) 7 D) 5

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x.

44) f(x) = , g(x) = + 15

A) Yes, no B) No, yes C) Yes, yes D) No, no

44)

45) f(x) = + 3 , g(x) = - 3

45)

A) No, yes B) Yes, no C) Yes, yes D) No, no

46)

f(x) = , g(x) = x

A) Yes, yes B) No, yes C) Yes, no D) No, no

46)

47) f(x) = , g(x) = 47)

A) Yes, yes B) No, yes C) No, no D) Yes, no

48) f(x) = + 6, g(x) =

A) No, yes B) Yes, yes C) No, no D) Yes, no

48)

Determine the difference quotient (h ≠ 0) for the function f. Simplify

completely.

49) f(x) = 3x - 14 49)

A) 3 B) -3h C) 14 D)

50) f(x) = + 11x - 1

50)

A) 6x + 11 B) 3x + 6 + 6h

C) 6x + 11 + 3h D) 6xh + 11h + 11

51) f(x) = 15 - 6

51)

A)

B) - xh - )

C) + 3xh + )

D) - 3x - h)

Consider the function h as defined. Find functions f and g such that (f ∘ g)(x) = h(x).

52)

h(x) =

A)

f(x) = , g(x) = - 5

C)

f(x) = , g(x) = -

B)

f(x) = , g(x) = x - 5

D)

f(x) = , g(x) = - 5

52)

53) h(x) = 53)

A) f(x) = , g(x) = 9x - 6 B) f(x) = , g(x) = 9x + 6

C) f(x) = - , g(x) = 9x + 6 D) f(x) = x, g(x) = 9x + 6

54)

h(x) = + 2

A)

f(x) = x, g(x) = + 2

C)

f(x) = x + 2, g(x) =

B)

f(x) = , g(x) = + 2

D)

f(x) = , g(x) = 2

54)

55)

h(x) =

A)

f(x) = , g(x) = 8x + 4

B) f(x) = 4, g(x) =

55)

C) f(x) = , g(x) = 4 D) f(x) = , g(x) = 8x + 4

56) h(x) = 56)

A) f(x) = , g(x) = -2

B) f(x) = 7 , g(x) = x - 2

C) f(x) = 7x - 2, g(x) = D)

f(x) = , g(x) = 7x - 2

57)

h(x) = 57)

A) f(x) = , g(x) = B)

f(x) = , g(x) =

C) f(x) = , g(x) = +

65

D) f(x) = + 65, g(x) =

Solve the problem.

58) Regrind, Inc. regrinds used typewriter platens. The cost to buy back eac h used

platen is

$ 1.80.

The fixed

cost to

run the

grinding

machine

is $ 192

per day.

If the

company

sells the

reground

platens

for $ 5.80,

how

many

must be

reground

daily to

break

even?

58)

A) 32 platens B) 48 platens

C) 25 platens D) 106 platens

59) Northwest Molded molds plastic handles which cost $ 0.30 per handle

to mold. The fixed cost to run the molding machine is $ 2128 per week.

If the company sells the handles for $ 2.30 each, how many handles

must be molded weekly to break even?

A) 1064 handles B) 818 handles

C) 709 handles D) 7093 handles

60) Midtown Delivery Service delivers packages which cost $ 1.70 per

package to deliver. The fixed cost to run the delivery truck is $ 100 per

day. If the company charges $ 6.70 per package, how many packages

must be delivered daily to break even?

A) 58 packages B) 11 packages

C) 13 packages D) 20 packages

61) A lumber yard has fixed costs of $ 1958.40 a day and marginal costs of $

0.69 per board-foot produced. The company gets per board-foot

sold. How many board-feet must be produced daily to break even?

A) 725 board-feet B) 2838 board-feet

C) 615 board-feet D) 1088 board-feet

62) Midtown Delivery Service delivers packages which cost $ 2.30 per

package to deliver. The fixed cost to run the delivery truck is $ 134 per

day. If the company charges $ 4.30 per package, how many packages

must be delivered daily to make a profit of ?

A) 58 packages B) 20 packages

C) 67 packages D) 77 packages

59)

60)

61)

62)

63) The cost of manufacturing clocks is given by C(x) = 39 + 34x - .

Also, it is known that in t hours the number of clocks that can be

produced is given by x = 9t, where Express C as a function

of t.

A) C(t) = 39 + 34t - 9 B) C(t) = 39 + 306t - 81t

C) C(t) = 39 + 306t - 81

D) C(t) = 39 + 34t +

63)

64) At Allied Electronics, production has begun on the X-15 Computer

Chip. The total revenue function is given by and the

total cost function is given by , where x represents the

number of boxes of computer chips produced. The total profit function,

P(x), is such that . Find P(x).

A) P(x) = + 47x - 18

B) P(x) = + 36x - 27

C) P(x) = + 47x - 9

D) P(x) = + 36x + 9


Chip. The total revenue function is given by and the

total profit function is given by , where x

represents the number of boxes of computer chips produced. The total

cost function, C(x), is such that Find C(x).

A) C(x) = 10x + 11 B) C(x) = 8x + 15

C) C(x) = 9x + 20 D) C(x) = + 16x + 15


Chip. The total cost function is given by and the total

profit function is given by , where x represents

the number of boxes of computer chips produced. The total revenue

function, R(x), is such that . Find R(x).

A) R(x) = 44x - B)

R(x) = 45x -

C) R(x) = 45x + D)

R(x) = 47x -

67) The radius r of a circle of known area A is given by r = , where

Find the radius and circumference of a circle with an area of

14.51 sq ft. (Round results to two decimal places.)

A) r = 2.15 ft, C = 13.50 ft B) r = 2.15 ft, C = 8.86 ft

C) r = 2.15 ft, C = 13.50 sq ft D) r = 4.62 ft, C = 29.02 ft

68) The volume of water added to a circular drum of radius r is given by

= 25t, where is volume in cu ft and t is time in sec. Find the

depth of water in a drum of radius 2 ft after adding water for 24 sec.

(Round result to one decimal place.)

A) 95.5 ft B) 6.9 ft C) 150.0 ft D) 47.7 ft

69) A retail store buys 200 VCRs from a distributor at a cost of $ 235 each

plus an overhead charge of $ 30 per order. The retail markup is 45% on

the total price paid. Find the profit on the sale of one VCR.

A) $ 105.75 B) $ 10,581.75

64)

65)

66)

67)

68)

69)

C) $ 105.68 D) $ 105.82

70) A balloon (in the shape of a sphere) is being inflated. The radius is

increasing at a rate of 14 cm per second. Find a function, r(t), for the

radius in terms of t. Find a function, V(r), for the volume of the balloon

in terms of r. Find (V ∘ r)(t).

70)

A)

(V ∘ r)(t) =

C)

(V ∘ r)(t) =

B)

(V ∘ r)(t) =

D)

(V ∘ r)(t) =

71) A stone is thrown into a pond. A circular ripple is spreading over the

pond in such a way that the radius is increasing at the rate of 4.3 feet

per second. Find a function, r(t), for the radius in terms of t. Find a

function, A(r), for the area of the ripple in terms of r.

A) (A ∘ r)(t) = 4.3π

B) (A ∘ r)(t) = 8.6π

C) (A ∘ r)(t) = 18.49π

D) (A ∘ r)(t) = 18.49 t

72) Ken is 6 feet tall and is walking away from a streetlight. The streetlight

has its light bulb 14 feet above the ground, and Ken is walking at the

rate of 3.6 feet per second. Find a function, d(t), which gives the

distance Ken is from the streetlight in terms of time. Find a function,

, which gives the length of Ken's shadow in terms of d. Then find

.

A) (S ∘ d)(t) = 3.42t B) (S ∘ d)(t) = 1.98t

C) (S ∘ d)(t) = 2.7t D) (S ∘ d)(t) = 6.08t

73) Ken is 6 feet tall and is walking away from a streetlight. The streetlight

has its light bulb 14 feet above the ground, and Ken is walking at the

rate of 5.3 feet per second. Find a function, d(t), which gives the

distance Ken is from the streetlight in terms of time. Find a function,

, which gives the length of Ken's shadow in terms of d. Then find

. What is the meaning of ?

A) (S ∘ d)(t) gives the length of Ken's shadow in terms of time.

B) (S ∘ d)(t) gives the length of Ken's shadow in terms of his distance

from the streetlight.

C) (S ∘ d)(t) gives the time in terms of Ken's distance from the

streetlight.

D) (S ∘ d)(t) gives the distance Ken is from the streetlight in terms of

time.

71)

72)

73)

1) C

2) B

3) D

4) B

5) A

6) C

7) A

8) D

9) A

10) A

11) A

12) C

13) D

14) C

15) D

16) D

17) B

18) A

19) D

20) D

21) D

22) C

23) C

24) D

25) B

26) A

27) A

28) D

29) D

30) C

31) C

32) C

33) C

34) B

35) C

36) D

37) A

38) D

39) A

40) C

41) B

42) B

43) D

44) C

45) D

46) D

47) C

48) B

49) A

50) C

51) C

52) D

53) B

54) C

55) A

56) D

57) C

58) B

59) A

60) D

61) D

62) D

63) C

64) C

65) B

66) B

67) A

68) D

69) D

70) D

71) C

72) C

73) A

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