Question 1

Suppose that   is directly proportional to the 5th power of   . Which one of the following equations expresses this proportionality? .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    E

Question 2

Which one of the following is the graph of   ?

Accepted Answer

A)    
B)    
C)  None of these options 
D)    
E)    
A)    
B)    
C)  None of these options 
D)    
E)    B

Question 3

Which one of the following graphs represents the function   ?

Accepted Answer

A)    
B)    
C)  None of these options 
D)    
E)    
A)    
B)    
C)  None of these options 
D)    
E)    B

Question 4

Suppose that   is inversely proportional to the cube root of   . Which one of the following is an equation that expresses this statement?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

If   and   , find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Determine the end behavior of   .

Accepted Answer

A)  As   and as   . 
B)  As     and as     . 
C)  As   and as     . 
D)  As   and as   . 
E)  As     and as   . 
A)  As   and as   . 
B)  As     and as     . 
C)  As   and as     . 
D)  As   and as   . 
E)  As     and as   .

Question 7

Determine the end behavior of the function   .

Accepted Answer

A)  As   and   . 
B)  As   and   . 
C)  As   and   . 
D)  As   and   . 
E)  As   and   . 
A)  As   and   . 
B)  As   and   . 
C)  As   and   . 
D)  As   and   . 
E)  As   and   .

Question 8

The loudness   of a sound (measured in decibels dB) is inversely proportional to the square of the distance   from the source of the sound. Suppose a person who is 4 ft from a hair dryer experiences a sound level of 60 dB. How loud is the hair dryer for a person 7 ft away? Round to the nearest tenth.

Accepted Answer

A)  0.1 dB 
B)  19.6 dB 
C)  1.2 dB 
D)  70.0 dB 
E)  960.0 dB 
A)  0.1 dB 
B)  19.6 dB 
C)  1.2 dB 
D)  70.0 dB 
E)  960.0 dB

Question 9

Suppose that   is directly proportional to the 4th power of   . If it is known that   when   , find the proportionality constant. Round to the nearest hundredth.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Use the graph below to find an approximation of   .

Accepted Answer

A)  -8 
B)  63 
C)  -2 
D)  71 
E)  79 
A)  -8 
B)  63 
C)  -2 
D)  71 
E)  79

Question 11

If   and   , find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Use the table below to find .

Accepted Answer

A)  -27 
B)  -1 
C)  -36 
D)  -12 
E)  12 
A)  -27 
B)  -1 
C)  -36 
D)  -12 
E)  12

Question 13

The mouse population in a small desert area is modeled by the function   where   is measured in days. When is the maximum population attained and what is the maximum population?

Accepted Answer

A)  After 175 days, the mouse population is 0. 
B)  After 9 days, the mouse population is 1,310. 
C)  After 84 days, the mouse population is 1,310. 
D)  After 84 days, the mouse population is 7,005. 
E)  After 9 days, the mouse population is 2,485. 
A)  After 175 days, the mouse population is 0. 
B)  After 9 days, the mouse population is 1,310. 
C)  After 84 days, the mouse population is 1,310. 
D)  After 84 days, the mouse population is 7,005. 
E)  After 9 days, the mouse population is 2,485.

Question 14

Which one of the following functions best models the data given in the table below.

Accepted Answer

A)  Exponential 
B)  Power 
C)  Quadratic 
D)  Linear 
E)  None of these options 
A)  Exponential 
B)  Power 
C)  Quadratic 
D)  Linear 
E)  None of these options

Question 15

Find the equation(s) of the vertical asymptote(s) of   .

Accepted Answer

A)      
B)      and     
C)      
D)      and     
E)      and     
A)      
B)      and     
C)      
D)      and     
E)      and

Question 16

Determine the behavior of the function   as   .

Accepted Answer

A)  As   ,   . 
B)  As   ,   . 
C)  As   ,   . 
D)  As   ,   . 
E)  As   ,   . 
A)  As   ,   . 
B)  As   ,   . 
C)  As   ,   . 
D)  As   ,   . 
E)  As   ,   .

Question 17

If   and   , find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Suppose that   is directly proportional to the 5th root of   . If   when   , find the proportionality constant. Round to the nearest hundredth.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Use the table below to find .

Accepted Answer

A)  -39 
B)    
C)    
D)  -380 
E)    
A)  -39 
B)    
C)    
D)  -380 
E)

Question 20

Use the graph below to find   .

Accepted Answer

A)  -42 
B)  83 
C)  -2 
D)  41 
E)  -1 
A)  -42 
B)  83 
C)  -2 
D)  41 
E)  -1

Suppose that is directly proportional to the 5th power of . Which one of the following equations expresses this proportionality? .

Which one of the following is the graph of ?

Which one of the following graphs represents the function ?

Suppose that is inversely proportional to the cube root of . Which one of the following is an equation that expresses this statement?

If and , find .

Determine the end behavior of .

Determine the end behavior of the function .

The loudness of a sound (measured in decibels dB) is inversely proportional to the square of the distance from the source of the sound. Suppose a person who is 4 ft from a hair dryer experiences a sound level of 60 dB. How loud is the hair dryer for a person 7 ft away? Round to the nearest tenth.

Suppose that is directly proportional to the 4th power of . If it is known that when , find the proportionality constant. Round to the nearest hundredth.

Use the graph below to find an approximation of .

If and , find .

Use the table below to find .

The mouse population in a small desert area is modeled by the function where is measured in days. When is the maximum population attained and what is the maximum population?

Which one of the following functions best models the data given in the table below.

Find the equation(s) of the vertical asymptote(s) of .

Determine the behavior of the function as .

If and , find .

Suppose that is directly proportional to the 5th root of . If when , find the proportionality constant. Round to the nearest hundredth.

Use the table below to find .

Use the graph below to find .

Data, Functions, and Models

Linear Functions and Models

Exponential Functions and Models

Logarithmic Functions and Exponential Modela

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Exam 6: Power, Polynomial, and Rational Functions

Suppose that is directly proportional to the 5th power of . Which one of the following equations expresses this proportionality? .

Which one of the following is the graph of ?

Which one of the following graphs represents the function ?

Suppose that is inversely proportional to the cube root of . Which one of the following is an equation that expresses this statement?

If and , find .

Determine the end behavior of .

Determine the end behavior of the function .

The loudness of a sound (measured in decibels dB) is inversely proportional to the square of the distance from the source of the sound. Suppose a person who is 4 ft from a hair dryer experiences a sound level of 60 dB. How loud is the hair dryer for a person 7 ft away? Round to the nearest tenth.

Suppose that is directly proportional to the 4th power of . If it is known that when , find the proportionality constant. Round to the nearest hundredth.

Use the graph below to find an approximation of .

If and , find .

Use the table below to find .

The mouse population in a small desert area is modeled by the function where is measured in days. When is the maximum population attained and what is the maximum population?

Which one of the following functions best models the data given in the table below.

Find the equation(s) of the vertical asymptote(s) of .

Determine the behavior of the function as .

If and , find .

Suppose that is directly proportional to the 5th root of . If when , find the proportionality constant. Round to the nearest hundredth.

Use the table below to find .

Use the graph below to find .

Data, Functions, and Models

Linear Functions and Models

Exponential Functions and Models

Logarithmic Functions and Exponential Modela

Quadratic Functions and Models

Systems of Equations and Data in Categories

Filters