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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
A Unit Circle Approach 4th Edition by Hornsby Link full download test bank : http://testbankcollection.com/download/test-bank-for-
a-graphical-approach-to-precalculus-with-limits-a-unit-circle-approach-4th-edition-
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manual-for-a-graphical-approach-to-precalculus-with-limits-a-unit-circle-approach-
4th-edition-by-hornsby-lial-rockswold/
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)
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]
D) Increasing on (-∞, 0]; Decreasing on [0, ∞)
12) 12)
A) Increasing on (-∞, -2]; Decreasing on [ -2, ∞)
B) 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 (-∞, ∞)
D) Increasing on [0, ∞); Decreasing on (-∞, 0]
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, ∞)
A) Increasing B) Decreasing
27)
28) f(x) = - 2x + 1; (1, ∞)
28)
A) Increasing B) Decreasing
29)
f(x) = ; (3, ∞) 29)
A) Increasing B) Decreasing
30)
f(x) = ; (-∞, 0)
A) Increasing B) Decreasing
30)
31) f(x) = ; (-∞, 4) 31)
A) Increasing B) Decreasing
24)
32) f(x) = ∣ x - 8∣ ; (-∞, 8) 32)
A) Increasing B) Decreasing
33)
f(x) = + 7; (0, ∞)
A) Increasing B) Decreasing
33)
34) f(x) = - ; (-3, ∞) 34)
A) Increasing B) Decreasing
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)
A) Neither even nor odd
B) Odd
C) Even
42)
40)
A) Even
B) Neither even nor odd
C) Odd
43) 43)
A) Odd
B) Neither even nor odd
C) Even
44)
42)
A) Neither even nor odd
B) Odd
C) Even
45) 45)
A) Neither even nor odd
B) Odd
C) Even
46)
44)
A) Even
B) Odd
C) Neither even nor odd
47) 47)
A) Neither even nor odd
B) Odd
C) Even
48)
46)
A) Odd
B) Neither even nor odd
C) Even
49) 49)
A) Neither even nor odd
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)
A) Even B) Odd C) Neither
48)
52) f(x) = -3 + 3x
52)
A) Even B) Odd C) Neither
53)
f(x) = -4 - 5 53)
A) Even B) Odd C) Neither
54)
f(x) = + + 6 54)
A) Even B) Odd C) Neither
55)
f(x) = + 4x - 2 55)
A) Even B) Odd C) Neither
56) f(x) = 56)
A) Even B) Odd C) Neither
57)
f(x) = -
A) Even B) Odd C) Neither
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)
A) y-axis B) Origin C) Neither
60) f(x) = 3 60)
A) y-axis B) Origin C) Neither
61)
f(x) = + 5 61)
A) y-axis B) Origin C) Neither
62)
f(x) = -2 + 9x 62)
A) y-axis B) Origin C) Neither
63)
f(x) = 3 + 2 63)
A) y-axis B) Origin C) Neither
64)
f(x) = + - 2 64)
A) y-axis B) Origin C) Neither
65)
f(x) = - 6x + 9 65)
A) y-axis B) Origin C) Neither
66) f(x)
= x
66)
+
A) y-axis B) Origin C) Neither
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)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
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
Provide an appropriate response.
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
=
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
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
by a factor of reflecting across the -axis, and shifting vertically
units in the direction.
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
by a factor of reflecting across the -axis, and shifting vertically
units in the direction.
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, ∞)
B) Increasing on [-1, ∞); Decreasing on (-∞, -1]
C) Increasing on (-∞, 1]; Decreasing on [1, ∞)
D) Increasing on [1, ∞); Decreasing on (-∞, 1]
61) 61)
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]
62) 62)
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, -∞)
63) 63)
A) Increasing on (-∞, 3]; Decreasing on (-∞, 3]
B) Increasing on [3, ∞); Decreasing on (-∞, 3]
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 (-∞, ∞)
D) Increasing on (-∞, 0]; Decreasing on [0, ∞)
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) =
Provide an appropriate response.
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
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
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)
Provide an appropriate response.
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)
Provide an appropriate response.
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
Provide an appropriate response.
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).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
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
65) At Allied Electronics, production has begun on the X-15 Computer
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
66) At Allied Electronics, production has begun on the X-15 Computer
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