Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the indicated function value.
1)
f(x) = x – 4, g(x) = x + 2
Find (f + g)(–3).
1)
A)
–12
B)
–8
C)
–4
D)
0
Find the requested value.
2)
f(x) = – 2x2– 1, g(x) = x – 3
Find f(–5) – g(–5).
2)
A)
–49
B)
–53
C)
–43
D)
56
Write the point–slope form of the line satisfying the conditions. Then use the point–slope form of the equation to write
the slope–intercept form of the equation in function notation.
3)
Passing through (–4, –26) and (3, 9)
3)
A)
f(x) = – 5x – 46
B)
f(x) =1
5x –126
5
C)
f(x) = – 1
5x –134
5
D)
f(x) =5x – 6
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
1
4)
f(x) =x2, g(x) =x2–3
4)
A)
g shifts the graph of f vertically
down 3units
B)
g shifts the graph of f vertically
up 3units
C)
g shifts the graph of f vertically
up 3units
D)
g shifts the graph of f vertically
down 3units
Find an equation for the line with the given properties.
5)
The solid line L contains the point (1, 4) and is perpendicular to the dotted line whose equation is
y =2x. Give the equation of line L in slope–intercept form.
5)
A)
y – 4 = 2(x – 1)
B)
y – 4 = – 1
2(x – 1)
C)
y =1
2x +9
2
D)
y = – 1
2x +9
2
Solve the problem.
6)
A firm making toaster ovens finds that the total cost, C(x), of producing x units is given by
C(x) =45x +390.
The revenue, R(x), from selling x units is determined by the price per unit times the number of units
sold, thus
R(x) =55x.
Find and interpret (R – C)(52).
6)
A)
–$130 loss, cost exceeds income
B)
$130 profit, income exceeds cost
C)
$91 profit, income exceeds cost
D)
$5590 profit, income exceeds cost
3
Find the indicated function value.
7)
x f(x)
–4–10
–2–2
0 6
214
422
Find f(–2)
7)
A)
14
B)
22
C)
–10
D)
–2
Evaluate the function.
8)
If g(x) =2x + 5, find g(a – 1).
8)
A)
2a + 8
B)
2a + 4
C)
2a – 2
D)
2a + 3
Use the given conditions to write an equation for the line in point–slope form.
9)
Passing through (10, 47) and (8, 39)
9)
A)
f(x) =4x +7
B)
f(x) = – 4x +87
C)
f(x) =1
4x +89
2
D)
f(x) = – 1
4x +99
2
Solve the problem.
10)
The function f(t) = – 0.15t2+0.5t +30.3 models a certain country’s population in millions, ages 65
and older, where t represents years after 2010. The function g(t) =0.56t2+11.32t +106.1 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).
10)
A)
Cost per person in thousands of dollars. $99.23 thousand
B)
Cost per person in thousands of dollars. $7.17 thousand
C)
Cost per person in thousands of dollars. $0.18 thousand
D)
Cost per person in thousands of dollars. $0.01 thousand
Find the slope then describe what it means in terms of the rate of change of the dependent variable per unit change in the
independent variable.
11)
The linear function f(x) =2.3x +20 represents the percentage of people, f(x), who graduated from
college x years after 1998.
11)
A)
m =2.3; the percentage of people graduating from college has increased at a rate of 2.3% per
year after 1998.
B)
m =20; the percentage of people graduating from college has increased at a rate of 20% per
year after 1998.
C)
m = – 2.3; the percentage of people graduating from college has decreased at a rate of 2.3%
per year after 1998.
D)
m =2.3; the percentage of people graduating from college has decreased at a rate of 2.3% per
year after 1998.
A
For the pair of functions, determine the domain of f +
g.
12)
f(x) =4x + 8, g(x) =2
x –4
12)
A)
(0, )
B)
( , )
C)
( , 4) or (4, )
D)
( , –2) or (–2, )
C
5
A
Find the slope and the y–intercept of the line.
13)
2x + 5y =25
13)
A)
m =5
2; b = – 5
B)
m =2
5; b =5
C)
m = – 2
5; b =5
D)
m = – 2
5; b = – 5
Find the domain of the function.
14)
f(x) =9x
x + 3
14)
A)
( , –3) or (–3, )
B)
( ,–3)
C)
( , 0) or (0, )
D)
( , )
A
Use intercepts and a checkpoint to graph the linear function.
15)
y –1
2x =2
15)
A)
(0, 2), (4, 0)
B)
(0, –4), (4, 0)
6
C
C)
(0, 2), (–4, 0)
D)
(0, 2), (–2, 0)
Use the slope and y–intercept to graph the linear function.
16)
8x –4y =32
16)
A)
B)
7
C)
D)
Find the slope.
17)
Find the slope of a line parallel to the line y =4.
17)
A)
0
B)
4
C)
1
4
D)
undefined
Find the slope and the y–intercept of the line.
18)
y = – 6x
18)
A)
m = – 1
6; b = 0
B)
m = 0; b = – 6
C)
m =6; b = 0
D)
m = – 6; b = 0
8
Solve the problem.
19)
From April through December, the stock price of QRS Company had a roller coaster ride. The chart
below indicates the price of the stock at the beginning of each month during that period. Find the
monthly average rate of change in price between June and September.
Stock Price of QRS Company from April through December
Price
(dollars)
Apr May Jun Jul Aug Sep Oct Nov Dec
Month
19)
A)
–$7.33 per month
B)
$11.00 per month
C)
–$11.00 per month
D)
$7.33 per month
Determine whether the relation is a function. Give domain and range of the relation.
20)
{(19, –4), (3, –3), (3, 0), (12, 3), (28, 5)}
20)
A)
function; domain: {19, 12, 3, 28}, range: {–4, –3, 0, 3, 5}
B)
function; domain: {–4, –3, 0, 3, 5}, range: {19, 12, 3, 28}
C)
not a function; domain: {–4, –3, 0, 3, 5}, range: {19, 12, 3, 28}
D)
not a function; domain: {19, 12, 3, 28}, range: {–4, –3, 0, 3, 5}
Given f(x) and g(x), find the following.
21)
f(x) =x2+ 3x and g(x) = x + 3. Find (f + g)(x) and (f + g)(–5).
21)
A)
x2+ 3x + 3; 13
B)
x2+ 4x + 3; 13
C)
2x2+ 6x; 20
D)
x2+ 4x + 3; 8
9
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
22)
f(x) =3x2, g(x) =3x2+3
22)
A)
g shifts the graph of f vertically
up 3units
B)
g shifts the graph of f vertically
up 3units
C)
g shifts the graph of f vertically
down 3units
D)
g shifts the graph of f vertically
down 3units
10
Use the given conditions to write an equation for the line in slope–intercept form.
23)
Passing through (4, 3) and parallel to the line whose equation is y = – 1
9x +7.
23)
A)
y = – 9x – 31
B)
y = – 1
9x –31
9
C)
y =1
9x –31
9
D)
y = – 1
9x +31
9
Given f(x) and g(x), find the following.
24)
f(x) =x2– 9x and g(x) = x – 7. Find f
g(x) and f
g(–1).
24)
A)
x2– 9x
x – 7 ; –5
4
B)
x2– 9x
x – 7 ; 10
7
C)
x – 9
–7; 10
7
D)
x2– 9x
x – 7 ; –10
7
Find the slope.
25)
Find the slope of a line perpendicular to the line 3x – 7y = – 9.
25)
A)
–7
3
B)
undefined
C)
–9
D)
7
3
Use the slope and y–intercept to graph the linear function.
26)
g(x) = – 3x + 1
26)
11
A)
B)
C)
D)
Graph the given functions in the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
27)
f(x) =2x2, g(x) =2x2–1
27)
12
A)
g is the graph of f shifted
down 1unit
B)
g is the graph of f shifted
up 1unit
C)
g is the graph of f shifted
down 1unit
D)
g is the graph of f shifted
up 1unit
Solve.
28)
The average value of a certain type of automobile was $15,900 in 2007 and depreciated to $9120 in
2011. Let y be the average value of the automobile in the year x, where x = 0 represents 2007. Write
a linear equation that models the value of the automobile in terms of the year x.
28)
A)
y = – 1695x +9120
B)
y = – 1695x +15,900
C)
y = – 1
1695 x – 9120
D)
y = – 1695x + 2340
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
13
29)
f(x) =x3, g(x) =x3–2
29)
A)
g shifts the graph of f vertically
down 2units
B)
g shifts the graph of f vertically
down 2units
C)
g shifts the graph of f vertically
up 2units
D)
g shifts the graph of f vertically
up 2units
14
Find the indicated function value.
30)
f(x) =3x2– 1, g(x) =2x2+ 4x –1
Find (f + g)(3).
30)
A)
37
B)
55
C)
57
D)
43
Use intercepts and a checkpoint to graph the linear function.
31)
4x –20y =8
31)
A)
0, –2
5, (–2, 0)
B)
0, –2
5, (2, 0)
C)
0, 2
5, (–2, 0)
D)
(0, 2), –2
5, 0
15
Use the given conditions to write an equation for the line in slope–intercept form.
32)
Passing through (5, 4) and parallel to the line whose equation is y = – 5x.
32)
A)
y = – 1
5x –29
5
B)
y = – 5x – 29
C)
y =5x – 29
D)
y = – 5x + 29
D
Find the domain of the function.
33)
f(x) =x
x2+12
33)
A)
(–12, )
B)
( , )
C)
( , –12) or (–12, )
D)
( , 0) or (0, )
B
Find the slope of the line.
34)
34)
A)
0
B)
3
C)
–8
D)
undefined
A
B
Find the domain of the function.
35)
f(x) = x2+ 4
35)
A)
( , –4) or (–4, )
B)
(–4, )
C)
[–4, )
D)
( , )
Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether
the line through the points rises, falls, is horizontal, or is vertical.
36)
(6, –9) and (–6, 4)
36)
A)
m = – 13
12 ; falls
B)
m =12
13 ; rises
C)
m =13
12 ; rises
D)
m = – 12
13 ; falls
A
Solve the problem.
37)
From April through December, the stock price of QRS Company had a roller coaster ride. The chart
below indicates the price of the stock at the beginning of each month during that period. Find the
monthly average rate of change in price between April and December.
Stock Price of QRS Company from April through December
Price
(dollars)
Apr May Jun Jul Aug Sep Oct Nov Dec
Month
37)
A)
–$6.25 per month
B)
$5.56 per month
C)
–$5.56 per month
D)
$6.25 per month
A
D
Use the graph to find the value.
38)
(fg)(6)
38)
A)
–8
B)
8
C)
6
D)
–6
Find the slope and the y–intercept of the line.
39)
3y – 4x = – 13
39)
A)
m =4
3; b = – 13
3
B)
m =4
3; b =13
3
C)
m = – 4
3; b = – 13
3
D)
m = – 3
4; b =13
3
Use the graph to find the indicated function value.
40)
y = f(x). Find f(4).
40)
A)
1.75
B)
13
C)
–4
D)
4
Determine if the graph represents y as a function of x.
41)
41)
A)
Not a function
B)
Function
Decide whether the relation is a function.
42)
{(–5, 8), (–2, –9), (1, 6), (6, 4)}
42)
A)
not a function
B)
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.
43)
Does the graph represent a function?
43)
A)
yes
B)
no
Decide whether the relation is a function.
44)
Women’s Shoe Sizes
USA 3 4 5 6 7 8 9
Japan 20 21 22 23 24 25 26
44)
A)
function
B)
not a function
A
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
45)
f(x) = x, g(x) = x +4
45)
20
A