Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the graph of the function f to its inverse f–1.
1)
1)
A)
B)
C)
D)
1
2)
2)
A)
B)
C)
D)
2
3)
3)
A)
B)
C)
D)
Determine whether the relation represents a function.
4)
{(–3, –4), (–2, 7), (–1, –1), (–1, 7)}
4)
A)
Not a function
B)
Function
3
Given f(x) and g(x), perform the indicated operation.
5)
f(x) =6x2+ 11x – 21; g(x) =x+ 3
Find f
g(x).
5)
A)
x – 7
B)
6x – 7
C)
6x + 7
D)
6x – 7 +5
x – 7 , x 7
Provide an appropriate response.
6)
Given that g(x) =5x + 1, graph g(x) using a solid line and its inverse using a dashed line.
6)
A)
B)
4
C)
D)
Find the inverse of the following one–to–one function.
7)
f(x) =7x
6x +7
7)
A)
f–1(x) =7x
6–7x
B)
f–1(x) =–7x
6x +7
C)
f–1(x) =7x
7–6x
D)
f–1(x) =7x
7+6x
Determine the domain and range of the function.
8)
x y
–4 1
–113
1 1
413
8)
A)
Domain: {1, 13, 1, 13}; range: {–4, –1, 1, 4}
B)
Domain: {–4, 1, –1, –1}; range: {1, 1, 4, 13}
C)
Domain: {–4, –1, 1}; range: {1, 13, 1}
D)
Domain: {–4, –1, 1, 4}; range: {1, 13, 1, 13}
Decide whether the relation is a function.
9)
{(–4, 5), (–3, 2), (3, 5), (8, 1)}
9)
A)
Function
B)
Not a function
Determine whether the graph represents a function.
10)
10)
A)
Not a function
B)
A function
5
Evaluate.
11)
Find (g + f )(3) given f(x) = –2x +5 and g(x) =4x2+2.
11)
A)
30
B)
37
C)
32
D)
35
Solve the problem.
12)
The function h described by h(t) = –16t2+33.1t + 124.26 gives the height of a ball thrown upward
with an initial speed of 33.1 feet per second from a 124.26 ft high window t seconds after it is
thrown. Find the height of the ball 1.4 seconds after it is thrown.
12)
A)
201.96 ft
B)
46.56 ft
C)
139.24 ft
D)
109.28 ft
13)
All items in an ice cream truck cost $0.91 per item. (a) Fill in the chart with the correct response for
the total cost C(x) if x items are purchased. (b) Write the linear function which gives C(x).
x C(x)
0
1
2
3
13)
A)
(a)
x C(x)
0 $0.91
1 $1.82
2 $2.73
3 $3.64
; (b) C(x) =0.91x + 0.91
B)
(a)
x C(x)
0$0.00
1 $0.91
2 $1.82
3 $2.73
; (b) C(x) =0.91x + 0.91
C)
(a)
x C(x)
0$0.00
1 $0.91
2 $0.91
3 $0.91
; (b) C(x) =0.91
D)
(a)
x C(x)
0$0.00
1 $0.91
2 $1.82
3 $2.73
; (b) C(x) =0.91x
Provide an appropriate response.
14)
If f is defined by {(6, –9), (5, –8), (3, –7), (1, –6)}, find f–1.
14)
A)
f–1: {(–8, –9), (–9, 3), (6, 5), (–7, –7)}
B)
f–1: {(–9, 6), (–8, 5), (–7, 3), (–6, 1)}
C)
f–1: {(–8, –9), (–6, 3), (6, 3), (–7, –7)}
D)
Not invertible
Determine the domain and range of the function.
15)
x–3 2 6 8 12
y 7 –3–8 7 –3
15)
A)
B)
C)
D)
Evaluate.
16)
Find (f + g)(–4) given f(x) = –2x3– 3x – 19 and g(x) = 2x – 6x2.
16)
A)
5
B)
17
C)
137
D)
7
6
Solve the problem.
17)
The function F described by F(C) =9
5C + 32 gives the Fahrenheit temperature corresponding to the
Celsius temperature C. Find the Fahrenheit temperature equivalent to 25°C.
17)
A)
212°F
B)
167°F
C)
122°F
D)
77°F
Given f(x) and g(x), find the composition.
18)
f(x) = 4x2+ 4x + 8; g(x) =4x – 4
Find (g
f)(x).
18)
A)
(g
f)(x) =16x2+ 16x + 36
B)
(g
f)(x) = 4x2+ 16x + 28
C)
(g
f)(x) = 4x2+ 4x + 4
D)
(g
f)(x) =16x2+ 16x + 28
Evaluate the function for the given value.
19)
f(x) =4x2+6x, f(2a)
19)
A)
16a2+12a
B)
28a
C)
8a2+12a
D)
16a2+6a
Decide whether the relation is a function.
20)
{(–8, 2), (–8, 8), (–1, –2), (5, 1), (9, –8)}
20)
A)
Function
B)
Not a function
Determine the domain and range of the function.
21)
{(8, –4), (1, –5), (5, –1), (0, 0)}
21)
A)
Domain: {8, 1, 5, 0}; range: {4, –5, –1, 0}
B)
Domain: {8, 1, 5, 0}; range: {–4, –5, –1, 0}
C)
Domain: {8, 1, 5}; range: {–4, –5, –1}
D)
Domain: {8, –1, 5, 0}; range: {–4, –5, –1, 0}
Find the inverse of the function represented by the set of ordered pairs.
22)
f: {(16, 1), (–7, 5), (6, 3)}
22)
A)
f–1: {(1, 16), (6, –7), (3, 5)}
B)
f–1: {(1, 16), (5, –7), (3, 6)}
C)
f–1: {(16, 5), (16, –7), (3, 6)}
D)
Not invertible
Determine whether the graph represents a function.
23)
23)
A)
Not a function
B)
A function
Decide whether the relation is a function.
24)
{(–9, 3), (–9, 5), (–1, –1), (5, 6), (9, 5)}
24)
A)
Function
B)
Not a function
7
Given f(x) and g(x), perform the indicated operation.
25)
f(x) =x2+ 7 – 6x; g(x) = –7x + 9
Find (f + g)(x).
25)
A)
x2– 13x + 16
B)
x2+ 2x + 16
C)
x2+ 2x + 3
D)
x2– 13x +17
Given f(x) and g(x), find the composition.
26)
f(x) = –6x + 4; g(x) =4x + 5
Find (g
f)(x).
26)
A)
(g
f)(x) = –24x + 21
B)
(g
f)(x) = –24x – 11
C)
(g
f)(x) =24x + 21
D)
(g
f)(x) = –24x + 34
Determine the domain and range of the function.
27)
{(4, –2), (7, –6), (3, –9), (6, –2)}
27)
A)
Domain: {–2, –6, –9}; range: {4, 7, 3, 6}
B)
Domain: {4, 7, 3, 6}; range: {–2, –6, –9, 6}
C)
Domain: {4, 7, 3, 6}; range: {–2, –6, –9}
D)
Domain: {4, 7, 3, –6}; range: {–2, –6, –9}
Provide an appropriate response.
28)
Graph the function f(x) = |x| – 1 for x 4, and identify its domain and range.
28)
A)
Domain: (–
, 4]; range: [1,
)
B)
Domain: (–
, 4); range: (–1,
)
8
C)
Domain: (–
, 4); range: (1,
)
D)
Domain: (–
, 4]; range: [–1,
)
Decide whether the relation is a function.
29)
{(–3, –3), (2, 6), (4, 9), (8, 6), (12, 9)}
29)
A)
Function
B)
Not a function
Evaluate.
30)
Find (f/g)(8) given f(x) = –8x +4 and g(x) =5x2+8.
30)
A)
–15
82
B)
–1
5
C)
–8
41
D)
–3
16
Find the inverse of the following one–to–one function.
31)
f(x) =x
8
31)
A)
f–1(x) = x –8
B)
f–1(x) =8– x
C)
f–1(x) =8
x
D)
f–1(x) =8x
Evaluate.
32)
Find (f · g)(4) given f(x) = –3x +8 and g(x) =7x2+ 9.
32)
A)
–448
B)
–1344
C)
–484
D)
–1452
Evaluate the function for the given value.
33)
Find f(–4) when f(x) =5x2– 3x – 2
33)
A)
94
B)
66
C)
90
D)
26
Provide an appropriate response.
34)
Consider the functions f(x) = –16x2– 10x and g(x) =14x2– 20x + 3. Find (f – g)(x).
34)
A)
–30x2– 30x – 3
B)
–20x2– 3
C)
–2x2– 30x + 3
D)
–30x2+ 10x – 3
Graph the function. Then identify its domain and range.
9
35)
f(x) = –|x – 3|
35)
A)
Domain: (–
,
); range: [0,
)
B)
Domain: (–
,
); range: (–
, 0]
C)
Domain: (–
,
); range: (–
, 0]
D)
Domain: (–
,
); range: (–
, –3]
Determine whether the relation is a function.
36)
x–3 2 4 7 12
y–9–1–4–9 3
36)
A)
A function
B)
Not a function
10
Solve the problem.
37)
The average price for a quart of orange juice between 2002 and 2012 can be approximated by
P(x) = 0.102(x – 2002) + 1.87, where x is the year. Evaluate P(2010) and interpret the result.
37)
A)
B)
C)
D)
Find the inverse of the function represented by the set of ordered pairs.
38)
f: {(2, 8), (–2, –8), (4, –6), (–4, 6)}
38)
A)
f–1: {(8, 2), (2, –2), (–6, 4), (6, –4)}
B)
f–1: {(8, 2), (–8, –2), (–6, –2), (6, –4)}
C)
f–1: {(8, 2), (–8, –2), (–6, 4), (6, –4)}
D)
Not invertible
Decide whether the relation is a function.
39)
{(–2, –7), (3, –7), (5, 4), (8, 2), (11, –6)}
39)
A)
Not a function
B)
Function
Evaluate the function for the given value.
40)
Given f(x) =1
2x +4, find f(–3).
40)
A)
–5
2
B)
11
2
C)
0
D)
5
2
41)
Find f(0) when f(x) = x2– 5x – 7
41)
A)
7
B)
–7
C)
0
D)
49
Solve the problem.
42)
It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond
using a certain bait is f(t) = 0.23t + 1, for t > 10. Find the number of fish that can be caught if you
fish for 20 minutes. Round your answer to the nearest whole number.
42)
A)
22
B)
12
C)
6
D)
24
Find the inverse of the following one–to–one function.
43)
f(x) =7x + 1
43)
A)
f–1(x) =x + 1
7
B)
f–1(x) =x – 1
7
C)
f–1(x) =x
7– 1
D)
Not invertible
Decide whether or not the functions are inverses of each other.
44)
f(x) = –3+4
x , g(x) =–4
x + 3
44)
A)
Inverses
B)
Not inverses
Provide an appropriate response.
45)
Consider the functions f(x) =5x2– 5x + 9 and g(x) =4x2+ 3x. Find (f + g)(x).
45)
A)
9x4– 2x2+ 9
B)
9x2– 5x + 12
C)
9x4+ 2x2– 9
D)
9x2– 2x + 9
11
Find the inverse of the following one–to–one function.
46)
f(x) =2x
46)
A)
f–1(x) =2+ x
B)
f–1(x) =2x
C)
f–1(x) =x
2
D)
f–1(x) =2
x
Decide whether the relation is a function.
47)
{(–4, 1), (–3, –6), (3, –8), (3, 4)}
47)
A)
Function
B)
Not a function
Given f(x) and g(x), find the composition.
48)
f(x) =x –9
3; g(x) =8x +4
Find (g
f)(21).
48)
A)
48
B)
688
C)
163
3
D)
36
Evaluate the function for the given value.
49)
Find f(2a) when f(x) =6x2+4x.
49)
A)
24a2+8a
B)
12a2+8a
C)
32a
D)
24a2+4a
Determine whether the function whose graph is shown is a one–to–one function.
50)
50)
A)
One–to–one
B)
Not one–to–one
12
Determine whether the graph represents a function.
51)
51)
A)
Not a function
B)
A function
Solve the problem.
52)
The cost C, in dollars, of having a dinner party catered by Elaine’s Kosher Catering Company can
be approximated by the function C(n) =55 +11n, where n is the number of people attending the
party. The banquet hall where the dinner will be located can hold no more than 150 people. Find
the domain of the function.
52)
A)
(–
, 150]
B)
[0, 150]
C)
[7, 55]
D)
(–
,
)
Provide an appropriate response.
53)
Determine whether the function whose graph is shown is one–to–one. If it is, sketch the graph of its
inverse using a dashed line.
53)
13
A)
One–to–one
B)
One–to–one
C)
One–to–one
D)
Not one–to–one
54)
Given f(x) =x and g(x) = 4x – 14, find (f
g)(14).
54)
A)
–42
B)
41
C)
42
D)
43
Determine whether the graph represents a function.
55)
55)
A)
A function
B)
Not a function
Graph the function. Then identify its domain and range.
14
56)
h(x) = |x| + 3
56)
A)
Domain: (–
,
); range: [0, –
)
B)
Domain: (–
,
); range: [–3,
)
C)
Domain: (–
,
); range: [3, –
)
D)
Domain: (–
,
); range: [3,
)
Decide whether or not the functions are inverses of each other.
57)
f(x) =2x – 2, g(x) =1
2x + 1
57)
A)
Inverses
B)
Not inverses
15
Solve the problem.
58)
A long distance telephone service provider charges a monthly service fee, given by the function
A(t) =0.1t +4.8, after t minutes. Find A–1(55).
58)
A)
598 minutes
B)
5.02 minutes
C)
502 minutes
D)
10.3 minutes
Determine whether the relation is a function.
59)
The number of tests in various classes:
Math 10
English 7
History 10
Biology 6
Psychology 3
59)
A)
Not a function
B)
A function
Evaluate.
60)
Find (g/f)(–4) given f(x) =2x2+ 14x + 3 and g(x) =3x – 6.
60)
A)
–1
7
B)
6
7
C)
–2
21
D)
1
3
Decide whether or not the functions are inverses of each other.
61)
f(x) =7
x + 4 , g(x) = –4+7
x
61)
A)
Inverses
B)
Not inverses
16
Given the graph of a one–to–one function, sketch the graph of its inverse.
62)
62)
A)
B)
C)
D)
Decide whether the relation is a function.
63)
{(–4, –5), (–2, –1), (–1, –1), (–1, 7)}
63)
A)
Not a function
B)
Function
17
Determine whether the function whose graph is shown is a one–to–one function.
64)
64)
A)
One–to–one
B)
Not one–to–one
Determine whether the graph represents a function.
65)
65)
A)
Not a function
B)
A function
Determine whether the function whose graph is shown is a one–to–one function.
66)
66)
A)
One–to–one
B)
Not one–to–one
18
Determine whether the relation is a function.
67)
67)
A)
Not a function
B)
A function
68)
68)
A)
A function
B)
Not a function
19
Graph the function. Then identify its domain and range.
69)
h(x) =3x
69)
A)
Domain: (–
,
); range: (–
,
)
B)
Domain: (–
,
); range: (–
,
)
C)
Domain: (–
,
); range: (–
,
)
D)
Domain: (–
,
); range: (–
,
)
20
Determine whether the graph represents a function.
70)
70)
A)
Not a function
B)
A function
Given f(x) and g(x), perform the indicated operation.
71)
f(x) = –3x + 1; g(x) =6x2– x – 7
Find (f · g)(x).
71)
A)
–18x3+ 3x2+ 20x – 7
B)
9x2+ 20x – 7
C)
–18x3+ 20x – 7
D)
–18x3+ 9x2+ 20x – 7
Provide an appropriate response.
72)
Given f(x) =x and g(x) =2x –3, find (g
f)(x).
72)
A)
2x –3
B)
2x –3
C)
2 x –3
D)
2x –3
Evaluate the function for the given value.
73)
Given f(x) =3x + 17, find f(19).
73)
A)
–40
B)
40
C)
3
D)
74
74)
Given f(x) = – x + 6 , find f(1).
74)
A)
7
B)
–7
C)
1
D)
–6
Determine whether the relation is a function.
75)
Credit card expenses on Jim‘s monthly bill:
Gas station $17.55
Restaurant $62.00
Grocery $87.99
Restaurant $64.50
Gas station $19.47
75)
A)
Not a function
B)
A function
21
Graph the function. Then identify its domain and range.
76)
g(x) =x2– 4
76)
A)
Domain: (–
,
); range: [–4,
)
B)
Domain: (–
,
); range: [0,
)
C)
Domain: (–
,
); range: [4,
)
D)
Domain: (–
,
); range: [0,
)
22
77)
h(x) = –3
77)
A)
Domain: (–
,
); range: {–3}
B)
Domain: {–3}; range: (–
,
)
C)
Domain: {–3}; range: (–
,
)
D)
Domain: (–
,
); range: {–3}
Evaluate the function for the given value.
78)
Find g(a – 1) when g(x) =2x – 3.
78)
A)
2a – 3
B)
1
2a – 3
C)
2a + 1
D)
2a – 5
Evaluate.
79)
Find (f · g)(3) given f(x) =x2+ 12x + 35 and g(x) =49 –x2.
79)
A)
120
B)
3280
C)
3201
D)
3200
23
Provide an appropriate response.
80)
Consider the functions f(x) =6x2+2x and g(x) =8x2–2x +1. Find (f ·g)(x).
80)
A)
48x4–12x2+8
B)
48x4+ 4x3+ 2x2
C)
48x4– 4x3+ 2x2+2x
D)
48x4+ 4x3+ 2x2+2x
Graph the function. Then identify its domain and range.
81)
f(x) =1
6x – 5
81)
A)
Domain: (–
,
); range: (–
,
)
B)
Domain: (–
,
); range: (–
,
)
C)
Domain: (–
,
); range: (–
,
)
D)
Domain: (–
,
); range: (–
,
)
24
Determine whether the function whose graph is shown is a one–to–one function.
82)
82)
A)
One–to–one
B)
Not one–to–one
Given f(x) and g(x), find the composition.
83)
f(x) = –9x – 7; g(x) = –3x2+ 4x – 6
Find (g
f)(–6).
83)
A)
–6445
B)
101
C)
41
D)
1235
Solve the problem.
84)
For children aged 5 to 15 years, the number of hours watching cartoons per week can be estimated
by the function H(s) = –0.5(s – 5) +17, where s is the age of the child. Find the domain of the
function.
84)
A)
(–
,
)
B)
[12, 17]
C)
[0.5, 17]
D)
[5, 15]
Determine the domain and range of the function.
85)
{(–3, –3), (–4, –4), (2, –1), (1, 5)}
85)
A)
B)
C)
D)
Find the inverse of the following one–to–one function.
86)
f(x) =x
4–9
86)
A)
f–1(x) =4x –36
B)
f–1(x) = x +13
C)
f–1(x) =4x +36
D)
f–1(x) =4x +9
25
Given the graph of a one–to–one function, sketch the graph of its inverse.
87)
87)
A)
B)
C)
D)
Given f(x) and g(x), perform the indicated operation.
88)
f(x) =2
x +2; g(x) =–2
x –2
Find (f + g)(x).
88)
A)
0
B)
2x2– 8
x2+4
C)
2x2
x2–4, x 2
D)
–8
x2–4, x –2, 2
26
Given f(x) and g(x), find the composition.
89)
f(x) =10
x6; g(x) =2– x,
Find (f
g)(x).
89)
A)
(f
g)(x) =2–10
x6
B)
(f
g)(x) =2–10
x6
C)
(f
g)(x) =10
2– x6
D)
(f
g)(x) =10
(2 – x)6
Determine the domain and range of the function.
90)
90)
A)
B)
C)
D)
Solve the problem.
91)
It has been determined that the number of fish f(x) that can be caught in x minutes in a certain pond
using a certain bait is f(x) = 0.28x + 1, for x > 10. Find f(20) and explain its meaning. Round to the
nearest whole number.
91)
A)
B)
C)
D)
27
Determine the domain and range of the function.
92)
92)
A)
B)
C)
D)
Determine whether the function whose graph is shown is a one–to–one function.
93)
93)
A)
One–to–one
B)
Not one–to–one
Determine whether the graph represents a function.
94)
94)
A)
Not a function
B)
A function
28
Solve the problem.
95)
Let f(x) compute the time in hours to travel x miles at 36 miles per hour. What is the interpretation
of f–1(6)?
95)
A)
The hours taken to travel 6 miles
B)
The miles traveled in 36 hours
C)
The hours taken to travel 36 miles
D)
The miles traveled in 6 hours
Graph the function. Then identify its domain and range.
96)
g(x) = – 1
2x +5, for x
0
96)
A)
Domain: [0,
); range: [5,
)
B)
Domain: ( , 0]; range: [5,
)
C)
Domain: [0,
); range: ( , 5]
D)
Domain: [0,
); range: ( ,
)
29
Determine whether the graph represents a function.
97)
97)
A)
A function
B)
Not a function
98)
98)
A)
Not a function
B)
A function
Evaluate the function for the given value.
99)
Given that f(x) =2x – 8 + 7, find f(3)
99)
A)
21
B)
9
C)
–9
D)
5
Evaluate.
100)
Find (g – f)(3) given f(x) =x2+ 13x + 36 and g(x) =16 –x2.
100)
A)
19
B)
–77
C)
–59
D)
77
30
Determine whether the relation is a function.
101)
101)
A)
Not a function
B)
A function
Decide whether the relation is a function.
102)
{(–6, 8), (–3, –4), (–1, –6), (2, 1)}
102)
A)
Function
B)
Not a function
Evaluate the function for the given value.
103)
Find f(1+1t) when f(x) =17.
103)
A)
17 +1t
B)
18
C)
17
D)
17 + 17t
Decide whether the relation is a function.
104)
{(2, –9), (2, –2), (6, 3), (9, –8), (12, 1)}
104)
A)
Function
B)
Not a function
Decide whether or not the functions are inverses of each other.
105)
f(x) =5x – 8, g(x) =x + 5
8
105)
A)
Inverses
B)
Not inverses
Solve the problem.
106)
To remodel a bathroom, a contractor charges $30 per hour plus material costs, which amount to
$4770. Therefore, the total cost to remodel the bathroom is given by f(x) =30x +4770 where x is the
number of hours the contractor works. Identify the inverse of f(x) and explain its meaning.
106)
A)
B)
C)
D)
31
Determine whether the graph represents a function.
107)
107)
A)
Not a function
B)
A function
32
Graph the function. Then identify its domain and range.
108)
g(x) = x + 3
108)
A)
Domain: (–
,
); range: (–
,
)
B)
Domain: (–
,
); range: (–
,
)
C)
Domain: (–
,
); range: (–
,
)
D)
Domain: (–
,
); range: (–
,
)
Provide an appropriate response.
109)
If g(x) =2x + 1, evaluate g(a + 1).
109)
A)
1
2a + 1
B)
2a – 1
C)
2a + 3
D)
2a + 1
33
Determine whether the relation is a function.
110)
110)
A)
A function
B)
Not a function
111)
Tips earned by servers at a restaurant one evening:
Mary $49
Lucy $31
Eric $29
Simon $49
Ruth $65
111)
A)
Not a function
B)
A function
Determine whether the function whose graph is shown is a one–to–one function.
112)
112)
A)
One–to–one
B)
Not one–to–one
Determine whether the relation is a function.
113)
A store’s “Employee of the Month” for various months:
Thompson April
McGraw May
Robinson June
Thompson July
Martinez August
113)
A)
A function
B)
Not a function
34
Given f(x) and g(x), perform the indicated operation.
114)
f(x) =18 x2– 11x; g(x) = –6x2– 5x + 3
Find (f – g)(x).
114)
A)
12x2– 16x + 3
B)
24x2– 16x – 3
C)
18x2– 3
D)
24x2– 6x – 3
Graph the function. Then identify its domain and range.
115)
h(x) =2–x2, for x 0
115)
A)
Domain: ( , 0]; range: ( ,
)
B)
Domain: ( , 0]; range: ( , 2]
C)
Domain: ( , 0]; range: [–2,
)
D)
Domain: [0,
); range: ( , 2]
35
Determine whether the relation is a function.
116)
x y
–2 4
–110
1 4
210
116)
A)
A function
B)
Not a function
Solve the problem.
117)
Suppose the sales of a particular brand of appliance are modeled by the linear function
S(x) =150x + 1400, where S(x) represents the number of sales in year x, with x = 0 corresponding to
2010. Find the number of sales expected in 2018 if this trend continues.
117)
A)
5200
B)
5050
C)
2450
D)
2600
36
Graph the function. Then identify its domain and range.
118)
f(x) = –6x – 5
118)
A)
Domain: (–
,
); range: (–
,
)
B)
Domain: (–
,
); range: (–
,
)
C)
Domain: (–
,
); range: (–
,
)
D)
Domain: (–
,
); range: (–
,
)
Provide an appropriate response.
119)
Given f(x) =x and g(x) =10x –12, find (f
g)(x).
119)
A)
10 x–12
B)
10x –12
C)
10x–12
D)
10x –12
Determine whether the relation is a function.
120)
x–6–6–1 3 8
y 2 1 1–5–6
120)
A)
A function
B)
Not a function
37
Find the inverse of the following one–to–one function.
121)
f(x) =8– x
121)
A)
f–1(x) =x
8
B)
f–1(x) =8– x
C)
f–1(x) = x –8
D)
Not invertible
Solve the problem.
122)
To remodel a bathroom, a contractor charges $30 per hour plus material costs, which amount to
$4530. Therefore, the total cost to remodel the bathroom is given by f(x) =30x +4530 where x is the
number of hours the contractor works. Find a formula for f–1(x). What does f–1(x) compute?
122)
A)
B)
C)
D)
Evaluate the function for the given value.
123)
g(x) =1
2x +6, g(–3)
123)
A)
0
B)
15
2
C)
–9
2
D)
9
2
Evaluate.
124)
Find (f – g)(3) given f(x) = –5x2+ 5 and g(x) = x – 3.
124)
A)
–40
B)
37
C)
–34
D)
–46
Determine whether the relation is a function.
125)
x y
4 7
5 6
4 1
5 5
125)
A)
A function
B)
Not a function
Solve the problem.
126)
The cost C, in dollars, of renting a car for a week from from Pricebusters Rent–A–Car can be
approximated by the function C(m) =0.11m +300, where m is the number of miles the car is driven.
Find the domain of the function.
126)
A)
[0,
)
B)
[300,
)
C)
(–
, 0.11]
D)
(–
,
)
Provide an appropriate response.
127)
Consider the functions f(x) =2x2+ 9x – 18 and g(x) =2x2– 3x. Find f
g(x).
127)
A)
x + 6
x, x 0
B)
x – 6
x, x –3
2, 0
C)
x + 6
x, x –3
2, 0
D)
x + 6
x, x 3
2, 0
38
Given f(x) and g(x), perform the indicated operation.
128)
f(x) =1
x –6; g(x) =1
x +12
Find f
g(x).
128)
A)
x +6
x –12, x 12
B)
12 + x
6–x, x 6
C)
x –12
x +6, x –6
D)
x +12
x –6, x 6
Given f(x) and g(x), find the composition.
129)
f(x) = 1 +9x; g(x) =1
x –9
Find (f
g)(–9).
129)
A)
1
2
B)
0
C)
–1
9
D)
Undefined
39
Graph the function. Then identify its domain and range.
130)
f(x) = –x2+ 5
130)
A)
Domain: (–
,
); range: [0,
)
B)
Domain: (–
,
); range: (–
, –5]
C)
Domain: (–
,
); range: (–
, 5]
D)
Domain: (–
,
); range: (–
, 0]
Find the inverse of the following one–to–one function.
131)
f(x) =5
x + 2
131)
A)
f–1(x) =–2x + 5
x
B)
f–1(x) =2+ 5x
x
C)
f–1(x) =x
2+ 5x
D)
Not invertible
40
Decide whether the relation is a function.
132)
{(–6, 5), (–1, 8), (3, 7), (5, 6)}
132)
A)
Function
B)
Not a function
Evaluate.
133)
Find (g
f)(2) given f(x) =x2+ 3x – 4 and g(x) =16 –x2.
133)
A)
8
B)
3
C)
2
D)
1
3
Determine whether the graph represents a function.
134)
134)
A)
Not a function
B)
A function
Solve the problem.
135)
Let f(x) compute the cost of a rental car after x days of use at $38 per day. What is the interpretation
of the solution of f–1(x) =279?
135)
A)
The cost of rental for 279 days
B)
The number of days rented for $38
C)
The cost of rental for 38 days
D)
The number of days rented for $279
41
Graph the function. Then identify its domain and range.
136)
f(x) =x +5, for x –5
136)
A)
Domain: [5,
); range: [0,
)
B)
Domain: ( , –5]; range: [0,
)
C)
Domain: [–5,
); range: [0,
)
D)
Domain: [–5,
); range: ( , 0]
42
Determine the domain and range of the function.
137)
137)
A)
B)
C)
D)
Find the domain and range of the function defined by the graph.
138)
138)
A)
B)
C)
D)
Find the inverse of the function represented by the set of ordered pairs.
139)
f: {(6, 3), (–2, 4), (–4, 5), (–6, 6)}
139)
A)
f–1: {(4, 3), (3, –4), (6, –2), (5, 5)}
B)
f–1: {(4, 3), (6, –4), (6, –4), (5, 5)}
C)
f–1: {(3, 6), (4, –2), (5, –4), (6, –6)}
D)
Not invertible
43
Evaluate.
140)
Find ( f
g)(5) given f(x) =x2+ 18x + 80 and g(x) =100–x2.
140)
A)
5
13
B)
15
13
C)
13
15
D)
13
5
Solve the problem.
141)
The function H described by H(x) = 2.75x + 71.48 can be used to estimate the height, in centimeters,
of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the
height of a woman whose humerus is 33.7 cm long.
141)
A)
21.195 cm
B)
107.93 cm
C)
40.53 cm
D)
164.155 cm
Provide an appropriate response.
142)
Find the inverse of the one–to–one function f(x) =2x + 3.
142)
A)
f–1(x) =x
2– 3
B)
f–1(x) = –2x – 3
C)
f–1(x) =x + 3
2
D)
f–1(x) =x – 3
2
44
Given the graph of a one–to–one function, sketch the graph of its inverse.
143)
143)
A)
B)
C)
D)
45
Determine whether the graph represents a function.
144)
144)
A)
Not a function
B)
A function
Evaluate the function for the given value.
145)
Find f(–1) when f(x) = x2+ 2x – 6
145)
A)
5
B)
–7
C)
–3
D)
9
46
Answer Key
Testname: C8
47
Answer Key
Testname: C8
48
Answer Key
Testname: C8
49