Question 1

For values of  , the function  grows faster than the function  .

Accepted Answer

A) True 
 B)False

Question 2

A cardboard box has a square base, with each edge of the base having length  inches, as shown in the figure. The volume of the box is determined by the function  . What is the domain of  in the context of this problem?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

Determine the end behavior of the function  .

Accepted Answer

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

Question 4

Find the equation of the horizontal asymptote of  .

Accepted Answer

A)    
B)   3 
C)    
D)    
E)

Question 5

If the rational function  has the vertical asymptote  , then as  ,  also.

Accepted Answer

A) True 
 B)False

Question 6

Determine the end behavior of the function  as  .

Accepted Answer

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

Question 7

Determine the behavior of  as  .

Accepted Answer

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

Question 8

Express the polynomial function  in complete factored form.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Which one of the following is the equation of the horizontal asymptote for  ?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Which one of the following is the graph of  .

Accepted Answer

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

Question 11

Which one of the following is a graph of the function  ?

Accepted Answer

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

Question 12

The function  is graphed below. Determine the x - and y -intercepts.

Accepted Answer

A)  The x -intercept is  ; the y -intercept is  . 
B)  There are no x -intercepts; the y -intercept is (0,  ). 
C)  There are no x -intercepts; there is no y -intercept. 
D)  The x -intercept is (0,  ); there is no y -intercept. 
E)  The x -intercepts are (0,  ) and (0,  ); the y -intercept is (0,  ).

Question 13

The area of a circle with radius  is given by the power function  . What happens to the area of the circle when the radius is multiplied by 3?

Accepted Answer

A)  The area increases by a factor of 9. 
B)  The area is also multiplied by 3. 
C)  The area increases by  . 
D)  Not enough information. 
E)  The area increases by  .

Question 14

The graph of a rational function is given. Determine the equation(s) of the vertical asymptote(s).

Accepted Answer

A)    and   
B)   
C)   
D)    and   
E)  There are no vertical asymptotes.

Question 15

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 3 ft from a hair dryer experiences a sound level of 75 dB. Find the proportionality constant and write the equation that expresses the inverse proportionality.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Which one of the following graphs represents the function  ?

Accepted Answer

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

Question 17

Determine the end behavior of the function  .

Accepted Answer

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

Question 18

Determine the end behavior of the function  .

Accepted Answer

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

Question 19

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Which one of the following graphs represents the function  ?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 6: Power, Polynomial, and Rational Functions

For values of , the function grows faster than the function .

A cardboard box has a square base, with each edge of the base having length inches, as shown in the figure. The volume of the box is determined by the function . What is the domain of in the context of this problem?

Determine the end behavior of the function .

Find the equation of the horizontal asymptote of .

If the rational function has the vertical asymptote , then as , also.

Determine the end behavior of the function as .

Determine the behavior of as .

Express the polynomial function in complete factored form.

Which one of the following is the equation of the horizontal asymptote for ?

Which one of the following is the graph of .

Which one of the following is a graph of the function ?

The function is graphed below. Determine the x - and y -intercepts.

The area of a circle with radius is given by the power function . What happens to the area of the circle when the radius is multiplied by 3?

The graph of a rational function is given. Determine the equation(s) of the vertical asymptote(s) .

Which one of the following graphs represents the function ?

Determine the end behavior of the function .

Determine the end behavior of the function .

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

Which one of the following graphs represents the function ?