Use the vertical line test to determine whether or not the graph is a graph of a function.
134)
134)
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.
135)
Between what two years is the difference in function values equal to 5%?
135)
A)
between 1995 and 2000
B)
between 1970 and 1975
C)
between 1980 and 1985
D)
between 1990 and 1995
Use the slope and y–intercept to graph the linear function.
61
136)
h(x) = – 2
5x – 3
136)
A)
B)
C)
D)
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
62
137)
f(x) = – 4x, g(x) = – 4x –4
137)
A)
g shifts the graph of f vertically
up 4units
B)
g shifts the graph of f vertically
down 4units
C)
g shifts the graph of f vertically
down 4units
D)
g shifts the graph of f vertically
up 4units
Use the graph of f to solve.
138)
List the two values of x for which f(x) = 0
138)
A)
2 and 3
B)
–2 and –3
C)
2 and –3
D)
–2 and 3
Use the vertical line test to determine whether or not the graph is a graph of a function.
139)
139)
A)
not a function
B)
function
Find the indicated function value.
140)
Find g(a + 1) when g(x) =2x + 3.
140)
A)
2a + 5
B)
2a + 2
C)
2a
D)
2a + 8
64
Use the graph to find the indicated function value.
141)
y = f(x). Find f(2)
141)
A)
3
B)
0.5
C)
–5
D)
5
Use the graph of f to solve.
142)
Find the domain of f.
142)
A)
[3, 6]
B)
(0, 6)
C)
( , )
D)
[0, 6]
Use the given conditions to write an equation for the line in slope–intercept form.
143)
Passing through (3, 2) and parallel to the line whose equation is y = – 4x +2.
143)
A)
y = – 4x + 14
B)
y = – 1
4x –7
2
C)
y = – 4x – 14
D)
y =4x – 14
Find the slope and the y–intercept of the line.
144)
x +14y –1 = 0
144)
A)
m =1
14 ; b =1
14
B)
m = 1; b = 1
C)
m = – 1
14 ; b =1
14
D)
m = – 14; b =14
Find the requested value.
145)
f(x) =4x – 7, g(x) =3x2+ 14x + 5
Find f
g(–5).
145)
A)
4
B)
–27
10
C)
3
10
D)
– 3
13
Find the indicated function value.
146)
Find f(2) when f(x) =2.
146)
A)
–4
B)
–2
C)
2
D)
0
147)
Find f(–5) when f(x) =x2+ 3
x3+ 8x.
147)
A)
–28
117
B)
–28
125
C)
–28
165
D)
–5
33
Graph the linear function.
148)
f(x) =2
148)
A)
B)
67
C)
D)
Use intercepts and a checkpoint to graph the linear function.
149)
50x + 20y =100
149)
A)
(0, –5), (2, 0)
B)
(0, 5), (–2, 0)
68
C)
(0, –5), (–2, 0)
D)
(0, 5), (2, 0)
Graph the given functions on the same rectangular coordinate system. Describe how the graph of g is related to the graph
of f.
150)
f(x) =3x2, g(x) =3x2–3
150)
A)
g shifts the graph of f vertically
up 3units
B)
g shifts the graph of f vertically
up 3units
69
C)
g shifts the graph of f vertically
down 3units
D)
g shifts the graph of f vertically
down 3units
Find the slope of the line.
151)
151)
A)
–3
2
B)
2
3
C)
3
2
D)
–2
3
Decide whether the relation is a function.
152)
{(–5, 1), (–3, –8), (3, –7), (3, 2)}
152)
A)
function
B)
not a function
Find the slope and the y–intercept of the line.
153)
x + y – 7 = 0
153)
A)
m = 1; b =7
B)
m = – 1; b =7
C)
m = – 1; b = – 7
D)
m = 0; b =7
Find the requested value.
154)
f(x) = x + 4, g(x) = x – 1
Find (f + g)(3).
154)
A)
3
B)
11
C)
1
D)
9
Solve the problem.
155)
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) =100x +7700.
The sales department estimates that the revenue, R(x), from selling x units will be
R(x) =110x,
but that no more than 894 units can be sold at that price. Find and interpret (R – C)(894).
155)
A)
$1664 profit, income exceeds cost
It is worth it to develop product.
B)
–$1240 loss, cost exceeds income
It is not worth it to develop product.
C)
$1240 profit, income exceeds cost
It is worth it to develop product.
D)
$195,440 profit, income exceeds cost
It is worth it to develop product.
Use the graph to find the indicated function value.
156)
y = f(x). Find f(–5)
156)
A)
11
B)
0.5
C)
3.5
D)
4.5
For the pair of functions, determine the domain of f +
g.
157)
f(x) =2x + 8, g(x) =2
x +4
157)
A)
( , )
B)
( , –4) or (–4, )
C)
(0, )
D)
( , –2) or (–2, )
B
72
B
Use the graph to identify domain and range.
158)
158)
A)
domain: ( , )
range: [1, )
B)
domain: (1, )
range: ( , )
C)
domain: ( , )
range: (1, )
D)
domain: [1, )
range: ( , )
Find the slope of the line that goes through the given points.
159)
(–5, –1), (3, –1)
159)
A)
0
B)
Undefined
C)
–1
4
D)
1
A
Find the requested value.
160)
f(x) = x + 4, g(x) =3x2+ 11x – 6
Find (fg)(–5).
160)
A)
–14
B)
–126
C)
36
D)
–621
A
Use the slope and y–intercept to graph the linear function.
73
A
161)
y = – 3x
161)
A)
B)
C)
D)
74
Find the domain of the function.
162)
f(x) =
–8x
x – 6
162)
A)
( , 6)
B)
( , 6) or (6, )
C)
( , )
D)
( , 0) or (0, )
Solve the problem.
163)
The following bar graph shows the average annual income for single mothers.
i) Determine a linear function that can be used to estimate the average yearly income for single
mothers from 2005 through 2010. Let t represent the number of years from 2005. (In other words,
2005 corresponds to t = 0, 2006 corresponds to t = 1, and so on.)
ii) Using the function from part i, determine the average yearly income for single mothers in 2009.
iii) Assuming this trend continues, determine the average yearly income for single mothers in 2017.
iv) Assuming this trend continues, in which year will the average yearly income for single mothers
reach $30,000?
163)
A)
i) I(t) = 775.8t + 24,269
ii) $28,148.00
iii) $33,578.60
iv) 2018
B)
i) I(t) = 775.8t + 24,269
ii) $27,372.20
iii) $33,578.60
iv) 2018
C)
i) I(t) = 775.8t + 24,269
ii) $27,372.20
iii) $33,578.60
iv) 2019
D)
i) I(t) = 770.8t + 24,269
ii) $27,352.20
iii) $33,518.60
iv) 2018
Rewrite the given equation in slope–intercept form by solving for y.
164)
4x + y =8
164)
A)
y = – 1
4x + 2
B)
y =4x + 8
C)
y =1
2x +1
8
D)
y = – 4x + 8
Find the indicated function value.
165)
Find g(a + 1) when g(x) =1
4x – 3.
165)
A)
a – 8
4
B)
a + 11
4
C)
a – 23
4
D)
a – 11
4
D
Use the given conditions to write an equation for the line in slope–intercept form.
166)
Passing through (3, 3) and perpendicular to the line whose equation is y =1
6x +3.
166)
A)
y = – 6x – 21
B)
y =6x – 21
C)
y = – 6x + 21
D)
y = – 1
6x –7
2
C
Decide whether the relation is a function.
167)
{(3, –9), (3, 7), (4, 1), (8, 7), (12, 1)}
167)
A)
not a function
B)
function
A
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.
168)
(–6, 2) and (–6, 6)
168)
A)
m = 0; horizontal
B)
m is undefined; vertical
C)
m = – 1; falls
D)
m = 1; rises
B
D
Solve the problem.
169)
The gas mileage, m, of a compact car is a linear function of the speed, s, at which the car is driven,
for 40
s 90. For example, from the graph we see that the gas mileage for the compact car is 45
miles per gallon if the car is driven at a speed of 40 mph.
i) Using the two points on the graph, determine the function m(s) that can be used to approximate
the graph.
ii) Using the function from part i, estimate the gas mileage if the compact car is traveling 75 mph. If
necessary, round to the nearest tenth.
iii) Using the function from part i, estimate the speed of the compact car if the gas mileage is 39
miles per gallon. If necessary, round to the nearest tenth.
169)
A)
i) m(s) = – 1
2s + 65
ii) 27.5 miles per gallon
iii) 52 mph
B)
i) m(s) = – 1
2s + 65
ii) 27.5 miles per gallon
iii) 57 mph
C)
i) m(s) = – 1
2s + 65
ii) 102.5 miles per gallon
iii) 52 mph
D)
i) m(s) =1
2s + 65
ii) 102.5 miles per gallon
iii) 52 mph
Find the indicated function value.
170)
f(x) =x2–3
4x – 5, g(x) =x3–1
2x2+ x
Find (f + g)(x).
170)
A)
2x3–5
8x2– 4x
B)
x3+1
4x2+1
8x – 5
C)
x3+1
2x2+1
4x – 5
D)
2x3–5
4x2– 4x
Find the domain of the function.
171)
f(x) =3x – 5
171)
A)
( , )
B)
( , 0) or (0, )
C)
( , 5) or (5, )
D)
(5, )
Decide whether the relation is a function.
172)
{(–2, 1), (3, 8), (6, 4), (9, 7), (11, –1)}
172)
A)
not a function
B)
function
Graph the equation in the rectangular coordinate system.
173)
4y = – 8
173)
78
A)
B)
C)
D)
Solve the problem.
174)
A truck rental company rents a moving truck one day by charging $31 plus $0.11 per mile. Write a
linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles
driven. What is the cost of renting the truck if the truck is driven 130 miles?
174)
A)
C(x) =0.11x –31; –$16.70
B)
C(x) =31x +0.11; $4030.11
C)
C(x) =0.11x +31; $45.30
D)
C(x) =0.11x +31; $32.43
For the pair of functions, determine the domain of f +
g.
175)
f(x) =5x
x –5, g(x) =3
x +7
175)
A)
( , –5) or (–5, 7) or (7, )
B)
( , –7) or (–7, 5) or (5, )
C)
( , )
D)
( , –7) or (5, )
Find the slope of the line that goes through the given points.
176)
(7, 9), (2, –5)
176)
A)
–7
2
B)
14
5
C)
5
14
D)
–2
7
B
Solve.
177)
A faucet is used to add water to a large bottle that already contained some water. After it has been
filling for 4 seconds, the gauge on the bottle indicates that it contains 14 ounces of water. After it
has been filling for 11 seconds, the gauge indicates the bottle contains 35 ounces of water. Let y be
the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation
that models the amount of water in the bottle in terms of x.
177)
A)
y =1
3x +38
3
B)
y = – 3x +26
C)
y =3x +24
D)
y =3x +2
D
Graph the linear function.
178)
h(x) =3
4x – 1
178)
B