Chapter 1
Page 41
132.
What is the equation for the graph obtained by shifting the graph of
3
yx=
vertically
upward by 2 units, followed by vertically stretching the graph by a factor of 5, followed
by reflecting the graph across the x-axis?
A)
3
5 10x−−
B)
3
52x−−
C)
2
10 2x+
D)
133.
If the graph of
()y f x=
shrinks vertically by a factor of 1/2, then shifts vertically by 6
units, then stretches vertically by a factor of 3, the resulting graph is the same as the
original graph.
A)
True
B)
False
Ans: B Learning Objectives: Understand stretches and shifts of graphs both
analytically and graphically. difficulty: medium section: 1.8
134.
Given the equation
3
()q x x=
, find and simplify
(2 ) ( )q x a q x++
.
135.
Given the equation
3
()q x x=
, find and simplify
2
( ) ( )q x q x a++
.
Learning Objectives: Find and/or evaluate composite functions given by formulas,
graphs or tables. difficulty: easy section: 1.8
136.
The cost of shipping r grams of material is given by the function
( ) 300 2C f r r= = +
.
Find a formula for the inverse function,
()rC
.
A)
( 300)/ 2rC=−
B)
300 2rC=+
C)
300 2rC= − −
D)
1
300 2
rC
=+
Ans: A Learning Objectives: Find and/or evaluate composite functions given by
formulas, graphs or tables. difficulty: medium section: 1.8
Ans: B Learning Objectives: Understand stretches and shifts of graphs both
analytically and graphically. difficulty: medium section: 1.8
Chapter 1
137.
For
2
( ) 4 4g x x x=+
and
( ) 2 1h x x=−
, find and simplify
( ( ))h g x
.
138.
For
2
( ) 5 2g x x x=+
and
( ) 5 1h x x=−
, find and simplify
( ( ))g h x
.
139.
Use the function in the graph to complete the table of values.
(-4, 0)
(-1, 2)(-1, 2)
(3, 1)(3, 1)
(4, 0)
1
2
3
-5 -4 -3 -2 -1 1 2 3 4 5
x
y
-4
-1
3
4
f(x)
0
2
1
0
f(x) + 4
-f(x)
-f(x) + 8
f(x)
0
2
1
0
f(x) + 4
4
6
5
4
-f(x)
0
-2
-1
0
-f(x) + 8
8
6
-9
8
Chapter 1
140.
Which of the following are power functions? Select all that apply.
A)
2
3
yx
=
B)
32
x
y=
C)
3yx=+
D)
3
(2 )yx=
141.
Use shifts of power functions to find a possible formula for the following graph.
A)
3
( 2) 4yx= + +
B)
3
( 2) 4yx= − +
C)
3
( 4) 2yx= + +
D)
3
( 4) 2yx= + −
142.
Simplify
2
(4)−
, leaving your answer as a fraction where appropriate.
Chapter 1
143.
The following table gives the values for
()y f x=
. It is possible that y could be
inversely proportional to x.
x
1
2
3
4
y
3
1.5
1
0.75
A)
True
B)
False
Ans: A Learning Objectives: Write and interpret a function describing a
proportional relationship. difficulty: easy section: 1.9
144.
Write a function that represents the following situation. The gravitational force, F,
between two bodies is inversely proportional to the square of the distance, d, between
them.
A)
2
F kd=
B)
2
1
Fk
d

=

C)
21
Fk
d

=

D)
2
F kd=
Ans: B Learning Objectives: Write and interpret a function describing a
proportional relationship. difficulty: hard section: 1.9
145.
The number of species, S, on an island is proportional to the square root of the area, A,
of the island. An island which has an area of 25 square miles contains 30 species.
How many species would be expected on an island of 9 square miles?
Ans:
18
Learning Objectives: Write and interpret a function describing a proportional
relationship. difficulty: medium section: 1.9
146.
Poiseuille’s law says that the rate of flow, F, of a gas through a cylindrical pipe is
proportional to the fourth power of the radius of the pipe, r. If the rate of flow is 400
cm3/sec in a pipe of radius 2 cm for a certain gas, how many cm3/sec flow through a
pipe with a 6 cm radius? Round to 2 decimal places.
Ans:
32,400.00
Learning Objectives: Write and interpret power functions given by tables, graphs, or
words. difficulty: medium section: 1.9
Chapter 1
Page 45
147.
A new music company wants to start selling collections of digital downloads. The
profit
(in thousands of dollars) is
2
π( ) 120 4p p p=−
, where p is the price of a
collection (in dollars). Use a graphing calculator to graph
π( )p
, and use the graph to
answer the following.
A. What is the maximum profit that can be obtained?
B. What is the price of a collection of downloads when the maximum profit is
obtained?
148.
A ball is thrown at time t = 0 and its height above ground t seconds after it is thrown is
given by
feet. Use a graphing calculator to graph
()ft
, and
use the graph to answer the following.
A. How high does the ball go?
B. How long is it in the air?
Part A:
A. 406 feet
Part B:
B. 10 seconds
Learning Objectives: Write and interpret power functions given by tables, graphs, or
words. difficulty: medium section: 1.9
Part A:
A. $900.00
Part B:
B. $15.00
Chapter 1
149.
In the following graph, the leading coefficient is ________(positive/negative)
Ans:
negative
Learning Objectives: Write and interpret power functions given by tables, graphs, or
words. difficulty: easy section: 1.9
150.
In the following graph, the minimum degree is _____.
Ans:
3
Learning Objectives: Write and interpret power functions given by tables, graphs, or
words. difficulty: easy section: 1.9
151.
Write a formula representing the function that says: The area of a circle is proportional
to the square of its radius.
Ans:
A=(pi)r^2
Chapter 1
152.
The illumination, I, of a candle is inversely proportional to the square of its distance, d,
from the object it illuminates. Write a formula that expresses this relationship.
Learning Objectives: Write and interpret a function describing a proportional
153.
Coulomb’s law says that the electrical force between two charged objects is directly
proportional to the product of the quantity of charge on the objects and inversely
proportional to the square of the distance between the objects. Let
1
q
and
2
q
be the
charge on the two objects. Let d be the distance between the objects and F be the
electrical force between them. Translate Coulomb’s Law into mathematical symbols.
A)
12
2
qq
Fd
=
B)
2
12
()
kd
Fqq
=−
C)
2
21
2
()k q q
Fd
−
=
D)
12
2
kq q
Fd
=
154.
As
x→
, the function
4
( ) 17f x x= − →
_____.
A)
−
B)
C)
neither of these
Ans: A Learning Objectives: Write and interpret power functions given by tables,
graphs, or words. difficulty: medium section: 1.9
155.
As
x→
, the function
7
( ) 5f x x=→
_____.
A)
B)
–
C)
neither of these
Ans: A Learning Objectives: Write and interpret power functions given by tables,
graphs, or words. difficulty: medium section: 1.9
Chapter 1
156.
Sketch global pictures of the functions
3
( ) 100f x x=−
,
4
( ) 28g x x=
, and
5
( ) 2h x x=
on
the same set of axes. Label each function on both ends so it is obvious which is which.
words. difficulty: medium section: 1.9
157.
Of the functions
3
( ) 100f x x=−
,
4
( ) 28g x x=
, and
5
( ) 2h x x=
, which has the largest
value as
x→
?
A)
3
( ) 100f x x=−
B)
4
( ) 28g x x=
C)
5
( ) 2h x x=
graphs, or words. difficulty: easy section: 1.9
158.
As
–x→
, the function
34
( ) 5 24 78 17f x x x x= + + − →
_____.
A)
−
B)
C)
neither of these
graphs, or words. difficulty: medium section: 1.9
Chapter 1
159.
As
–x→
, the function
5 4 2
( ) 5 30 2 8 100f x x x x x= − + − + →
_____.
A)
–
B)
C)
neither of these
graphs, or words. difficulty: easy section: 1.9
160.
Assume that the function shown in the following table is periodic. What is the amplitude
of the function?
x
1
2
3
4
5
6
7
8
9
()fx
-2
0
-2
-4
-2
0
-2
-4
-2
Ans:
2
value at a point. difficulty: easy section: 1.10
161.
Assume that the function shown in the following table is periodic. What is
(12)f
?
x
1
2
3
4
5
6
7
8
9
()fx
-2
0
-2
-4
-2
0
-2
-4
-2
Ans:
162.
At high tide, the water level is 6 feet below a certain pier. At low tide, the water level
is 18 feet below the pier. Assuming sinusoidal behavior, let
()ft
= the water level
relative to the pier, at time t (in hours). At t = 0 the water is -12 feet and falling until it
reaches the first low tide at t = 3. Give a formula for
()ft
.
words. difficulty: medium section: 1.10
Chapter 1
163.
In nature, the populations of two animals, one of which preys upon the other (such as
foxes and rabbits) are observed to oscillate with time, and are found to be well
approximated by trigonometric functions. The population of foxes is shown in the
graph below. Find the period.
Chapter 1
164.
In nature, the populations of two animals, one of which preys upon the other (such as
foxes and rabbits) are observed to oscillate with time, and are found to be well
approximated by trigonometric functions. The population of foxes is shown in the
graph below. How many foxes will there be in 15 months?
Chapter 1
Page 52
165.
If
siny A Bx C=+
defines the function graphed in the following figure, then A =_____,
B =_____, and C =_____.
166.
If
( ) sin πk t A B t C=+
defines the function graphed in the following figure, then A
=_____, B =_____, and C =_____.
Chapter 1
167.
The size of a bird population on an island can be described by a sinusoidal graph. The
number of birds on the island decreased from a maximum of 20,000 in 1943 to a
minimum of 12,000 in 1989, and then began increasing again. In what year will the
population begin decreasing again?
168.
The size of a bird population on an island can be described by a sinusoidal graph. The
number of birds on the island decreased from a maximum of 20,000 in 1943 to a
minimum of 12,000 in 1989, and then began increasing again. Find a function that
describes this behavior and use it to estimate the number of birds on the island in 2012.
Round to the nearest whole number.
169.
What value of B would you use if
sin Bt
was to model a periodic function with period 1
year where t is measured in months? Round to 4 decimal places.
170.
What value of B would you use if
sin Bt
was to model a periodic function, where t is
measured in hours and the period is 1 day? Round to 4 decimal places.
Chapter 1
171.
Give a formula for the following sinusoidal function as a transformation of
( ) sin( )f t t=
.
A)
( )
( ) 2sin 3f t t=−
B)
( ) 2sin 3
t
ft 
=− 

C)
( )
( ) 2sin 3f t t=
D)
( ) 2sin 3
t
ft 
=

172.
Give a formula for the following sinusoidal function as a transformation of
( ) cos( )f t t=
.
A)
9π
( ) 2cos 3 2
f t t

=+


B)
9π
( ) 2cos 3 2
f t t

=−


C)
9π
( ) 2cos 32
t
ft 
=+


D)
9π
( ) 2cos 32
t
ft 
=−

