Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
question.
Provide an appropriate response.
1)
1)
A function f models the percentage of attendance at weekly welfare–to–work meetings
as a function of number of continuous weeks an employee stays at the same job. The
graph of f is shown in the figure.
a. Explain why f has an inverse that is a function.
b. Find f(55).
c. Describe in practical terms the meaning of f–1(30).
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
Decide whether the relation is a function.
2)
2)
{(1, 3), (3, –6), (5, –9), (7, 6), (11, 3)}
A)
not a function
B)
function
Use the vertical line test to determine whether or not the graph is a graph of a function.
3)
3)
A)
not a function
B)
function
Use the graph to find the indicated function value.
4)
4)
y = f(x). Find f(4)
A)
–9
B)
7
C)
1.5
D)
9
Find the composition.
5)
If f(x) =6x2+4x and g(x) =3x, find (f
g)(x).
5)
A)
18x2+12x
B)
18x3+12x2
C)
54x2+12x
D)
6x2+7
6)
If f(x) = – 8
x and g(x) =7
x, find (f
g)(x).
6)
A)
–7x
8
B)
–8x
7
C)
–7
8x
D)
–8
7x
Decide whether the relation is a function.
7)
7)
Women’s Shoe Sizes
USA 3 4 5 6 7 8 9
Japan 20 21 22 23 24 25 26
A)
not a function
B)
function
Use the graph to find the value.
8)
8)
(fg)(–3)
A)
8
B)
–15
C)
15
D)
–8
Find the composition.
9)
If f(x) =x – 9
6 and g(x) =6x + 9, find (g
f)(x).
9)
A)
x + 18
B)
x –3
2
C)
6x + 45
D)
x
Use the vertical line test to determine whether or not the graph is a graph of a function.
10)
10)
A)
not a function
B)
function
Find the composition.
11)
If f(x) =x2– 3 and g(x) =x2– 12, find (g
f)(x).
11)
A)
x4– 6x2– 3
B)
x2+ 141
C)
x2– 3
D)
x4– 24x2+ 141
Find the indicated function value.
12)
12)
f(x) =5– 8x, g(x) = – 3x + 8
Find (f + g)(x).
A)
–5x + 13
B)
–3x + 5
C)
–11x + 13
D)
2x
Find the domain and range.
13)
13)
{(1,7), (–1,–9), (6,1), (6,–6)}
A)
domain = {–1, 1, 6}; range = {–9, 7, 1, –6}
B)
domain = {–9, 7, 1, –6}; range = {–1, 1, 6}
C)
domain = {–1, 1, 6, 16}; range = {–9, 7, 1, –6}
D)
domain = {–1, 1, 6, –6}; range = {–9, 7, 1, –6}
The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the
graph to answer the question.
14)
14)
If f represents the function, find f(2010).
A)
approximately 31%
B)
approximately 25.5%
C)
approximately 24%
D)
approximately 29%
Find the indicated function value.
15)
Find f(0) when f(x) =x2– 2x +
7.
15)
A)
–7
B)
7
C)
0
D)
49
Use the graph to identify domain and range.
16)
16)
A)
domain: [4,
)
range: ( ,
)
B)
domain: ( ,
)
range: [4,
)
C)
domain: ( ,
)
range: (4,
)
D)
domain: (4,
)
range: ( ,
)
Solve the problem.
17)
17)
A firm is considering a new product. The accounting department estimates that the total cost,
C(x), of producing x units will be
C(x) =80x +7870.
The sales department estimates that the revenue, R(x), from selling x units will be
R(x) =90x,
but that no more than 300 units can be sold at that price. Find and interpret (R – C)(300).
A)
$58,870 profit, income exceeds cost
It is worth it to develop product.
B)
$1087 profit, income exceeds cost
It is worth it to develop product.
C)
–$4870 loss, cost exceeds income
It‘s not worth it to develop product.
D)
$4870 profit, income exceeds cost
It is worth it to develop product.
Use the vertical line test to determine whether or not the graph is a graph of a function.
18)
18)
A)
function
B)
not a function
The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the
graph to answer the question.
19)
19)
If f(x) =15%, what year is represented by x?
A)
1995
B)
1985
C)
1980
D)
1990
20)
20)
Does the graph represent a function?
A)
yes
B)
no
Find the indicated function value.
21)
Find f(–1) when f(x) =x2– 2x + 4.
21)
A)
–1
B)
3
C)
–5
D)
7
Find the domain and range.
22)
22)
{(–4, 13), (–3, 6), (0, –3), (3, 6), (5, 22)}
A)
domain: {13, 6, –3, 22}; range: {–4, –3, 3, 5}
B)
domain: {13, 6, –3, 22}; range: {–4, –3, 0, 3, 5}
C)
domain: {–4, –3, 3, 5}; range: {13, 6, –3, 22}
D)
domain: {–4, –3, 0, 3, 5}; range: {13, 6, –3, 22}
23)
23)
{(–1,3), (–3,–9), (9,–3), (9,–1)}
A)
domain = {–1, 9, –3, –9}; range = {3, –3, –9, –1}
B)
domain = {–1, 9, –3}; range = {3, –3, –9, –1}
C)
domain = {–1, 9, –3, 19}; range = {3, –3, –9, –1}
D)
domain = {3, –3, –9, –1}; range = {–1, 9, –3}
Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.
24)
24)
f(x) = x +4 and g(x) = x –4
A)
inverses
B)
not inverses
9
Use the graph to identify domain and range.
25)
25)
A)
domain: ( ,
)
range:(0,
)
B)
domain: ( ,
)
range: ( ,
)
C)
domain: (0,
)
range: ( ,
)
D)
domain: (0,
)
range: (0,
)
Find the indicated function value.
26)
Find g(a – 1) when g(x) =1
5x – 5.
26)
A)
a – 30
5
B)
a + 26
5
C)
a – 51
5
D)
a – 26
5
Decide whether the relation is a function.
27)
27)
{(3, –3), (3, 3), (6, 9), (8, 8), (10, –7)}
A)
function
B)
not a function
Find the domain and range.
28)
28)
{(12,1), (–8,7), (10,2), (8,5)}
A)
domain = {5, 2, 1, 7}; range = {8, 10, 12, –8}
B)
domain = {8, 10, 12, –8}; range = {5, –1, 2, 1, 7}
C)
domain = {8, 10, 12, –8}; range = {5, 5, 2, 1, 7}
D)
domain = {8, 10, 12, –8}; range = {5, 2, 1, 7}
Solve the problem.
29)
The function f(t) = – 0.12t2+0.5t +30.5 models a certain country’s population in millions, ages 65
and older, where t represents years after 2010. The function g(t) =0.51t2+11.34t +106.7 models
the total yearly cost of the government’s health insurance program in billions of dollars, where t
represents years after 2010. What does the function g
f represent? Find g
f(15).
29)
A)
Cost per person in thousands of dollars. $0.03 thousand
B)
Cost per person in thousands of dollars. $0.17 thousand
C)
Cost per person in thousands of dollars. $35.60 thousand
D)
Cost per person in thousands of dollars. $8.26 thousand
Determine if the graph represents a function that has an inverse function.
30)
30)
A)
has an inverse
B)
does not have an inverse
31)
31)
A)
has an inverse
B)
does not have an inverse
Express the interval in set builder notation and graph the interval on a number line.
32)
32)
[2.5,
)
A)
{x x 2.5}
B)
{x x <2.5}
C)
{x x >2.5}
D)
{x x 2.5}
33)
33)
(–3,
)
A)
{x x > – 3 }
B)
{x x –3 }
C)
{x x –3 }
D)
{x x > – 3 }
Find the domain of the function.
34)
34)
f(x) = – 5x + 9
A)
( ,
)
B)
( , –9) or (–9,
)
C)
( , 0) or (0,
)
D)
(–9,
)
Use the graph to identify domain and range.
35)
35)
A)
domain: {–2}
range: ( ,
)
B)
domain: ( ,
)
range: {–2}
C)
domain: {–2}
range: (0,
)
D)
domain: (0,
)
range: {–2}
Use the vertical line test to determine whether or not the graph is a graph of a function.
36)
36)
A)
function
B)
not a function
Given f(x) and g(x), find the following.
37)
f(x) =x2– 5x and g(x) = x + 6. Find f
g(x) and f
g(–2).
37)
A)
x2– 5x
x + 6 ; –7
6
B)
x2– 5x
x + 6 ; 7
3
C)
x – 5
6; –7
6
D)
x2– 5x
x + 6 ; 7
2
Find the inverse of the one–to–one function.
38)
38)
f(x) = x – 11
A)
f–1(x) = – 11x
B)
f–1(x) =x
–11
C)
f–1(x) = x + 11
D)
f–1(x) =11x
Find the domain and range.
39)
39)
{(1, –2), (–3, –1), (–3, 0), (–2, 1), (6, 3)}
A)
domain: {1, –2, –3, 6}; range: {–2, –1, 0, 1, 3}
B)
domain: {1, –2, –3, 6}; range: {–2, –1, 1, 3}
C)
domain: {–2, –1, 1, 3}; range: {1, –2, –3, 6}
D)
domain: {–2, –1, 0, 1, 3}; range: {1, –2, –3, 6}
Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.
40)
f(x) =2
x +6 and g(x) =6
x–2
40)
A)
inverses
B)
not inverses
Find the indicated function value.
41)
41)
f(x) =3x – 3, g(x) = – 4x – 5
Find (f + g)(–5).
A)
–3
B)
–23
C)
2
D)
–33
Find the composition.
42)
If f(x) =5x2– 4x and g(x) =4x, find (g
f)(x).
42)
A)
20x3– 16x2
B)
5x2– 8
C)
20x2– 16x
D)
80x2– 4x
Use the graph of the function to draw the graph of the inverse function.
43)
43)
A)
B)
Use the vertical line test to determine whether or not the graph is a graph of a function.
44)
44)
A)
not a function
B)
function
45)
45)
A)
not a function
B)
function
Determine if the graph represents a function that has an inverse function.
46)
46)
A)
does not have an inverse
B)
has an inverse
Find the indicated function value.
47)
47)
x f(x)
–5–6
–3 0
0 9
318
524
For what value of x is f(x) =9?
A)
–3
B)
–5
C)
0
D)
3
Determine whether the relation is a function. Give domain and range of the relation.
48)
48)
{(1, –4), (–3, –3), (–3, 0), (6, 3), (22, 5)}
A)
not a function; domain: {1, 6, –3, 22}, range: {–4, –3, 0, 3, 5}
B)
function; domain: {1, 6, –3, 22}, range: {–4, –3, 0, 3, 5}
C)
not a function; domain: {–4, –3, 0, 3, 5}, range: {1, 6, –3, 22}
D)
function; domain: {–4, –3, 0, 3, 5}, range: {1, 6, –3, 22}
Given f(x) and g(x), find the following.
49)
f(x) =x2– 3x and g(x) = x + 3. Find (f – g)(x) and (f – g)(3).
49)
A)
x2– 4x – 3; –6
B)
x2– 4x – 3; –3
C)
x2– 3x – 3; –6
D)
–3x – 3; –12
Decide whether the relation is a function.
50)
50)
Tallest Roller Coaters in U.S. Amusement Parks
Amusement Park Name Park A Park A Park B Park C Park B Park A
Coaster Height (feet) 72 69 65 64 60 57
A)
function
B)
not a function