Question 1

Determine the equations of any horizontal and vertical asymptotes of  .
A) horizontal:  ; vertical: 
B) horizontal:  ; vertical: 
C) horizontal:  ; vertical: 
D) horizontal:  ; vertical: 
E) horizontal:  ; vertical: none

Accepted Answer

B

Question 2

Given  :
a. Determine the domains of  .
b. Simplify  and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.

Accepted Answer

a. Domain of  : all real numbers except -4
Domain of  : all real numbers
b.  ; no vertical asymptotes
c.
d. The graph of   except when  . Because the factor  canceled, there is a hole in the graph of  when  .

Question 3

Given  :
a. Determine the domains of  .
b. Simplify  and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.

Accepted Answer

a. Domain of  : all real numbers except  Domain of  : all real numbers except 0
b.  vertical asymptote  c.
d. The graph of   except when  . Because the factor  canceled, there is a hole in the graph of  when  .

Question 4

Find the domain of  .
A) all real numbers except 
B) all real numbers except 
C) all real numbers except 
D) all real numbers except 
E) all real numbers

Accepted Answer

The answer of Find the domain of  .
A) all...

Question 5

Find the domain of  .
A) all real numbers
B) all real numbers except 
C) all real numbers except 
D) all real numbers except 
E) all real numbers except

Accepted Answer

The answer of Find the domain of  .
A) all...

Question 6

Determine the equations of any horizontal and vertical asymptotes of  .
A) horizontal: none; vertical: none
B) horizontal:  ; vertical: 
C) horizontal:  ; vertical: 
D) horizontal:  ; vertical: 
E) horizontal:  ; vertical:

Accepted Answer

The answer of Determine the equations of any horizontal and...

Question 7

Determine the zeros (if any) of the rational function  .
A) 
B) no zeros
C) 
D) 
E)

Accepted Answer

The answer of Determine the zeros (if any) of the...

Question 8

Determine the zeros (if any) of the rational function  .
A) 
B) no zeros
C) 
D) 
E)

Accepted Answer

The answer of Determine the zeros (if any) of the...

Question 9

Determine the equations of the vertical and horizontal asymptotes of the graph of the function  .
A) horizontal:  ; vertical: 
B) horizontal:  ; vertical: 
C) horizontal:  ; vertical: 
D) horizontal:  ; vertical: 
E) horizontal:  ; vertical:

Accepted Answer

The answer of Determine the equations of the vertical and...

Question 10

Determine the equations of any horizontal and vertical asymptotes of  .
A) horizontal:  ; vertical: 
B) horizontal:  ; vertical: none
C) horizontal:  ; vertical: 
D) horizontal: none; vertical: none
E) horizontal:  ; vertical: none

Accepted Answer

The answer of Determine the equations of any horizontal and...

Question 11

Given  :
a. Determine the domains of  .
b. Simplify  and find any vertical asymptotes.
c. Complete the table.  d. Explain how the two functions differ.

Accepted Answer

The answer of Given  :
a. Determine the domains of...

Question 12

Determine the zeros (if any) of the rational function  .
A) 
B) 
C) 
D) 
E) no zeros

Accepted Answer

The given rational function is a constant function, which means it does not depend on the variable x. Therefore, it cannot have any zeros. The correct answer is choice E, "no zeros".

Question 13

The graph of the function  is shown below. Determine the vertical and horizontal asymptotes of its graph. 
A) horizontal:  
B) horizontal:  
C) horizontal:  
D) horizontal:  
E) horizontal:

Accepted Answer

The answer of The graph of the function  is...

Question 14

Determine the equations of any horizontal and vertical asymptotes of  .
A) horizontal:  ; vertical: 
B) horizontal:  ; vertical: 
C) horizontal:  ; vertical: none
D) horizontal:  ; vertical: 
E) horizontal:  ; vertical:

Accepted Answer

There is a horizontal asymptote when the degree of the numerator and denominator are the same. In this case, both the numerator and denominator have a degree of 2. Therefore, there is a horizontal asymptote at y = (leading coefficient of numerator) / (leading coefficient of denominator) = 11/(-6) = -11/6 = -1.833...

There is a vertical asymptote when the denominator equals zero. In this case, the denominator is (x-3)(x+2). Therefore, there are vertical asymptotes at x = 3 and x = -2. None of the other answer choices have the correct horizontal and vertical asymptotes.

Question 15

The graph of the function  is shown below. Determine the domain. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The graph of the function  is...

Question 16

Determine the domain of  .
A) all real numbers except 
B) all real numbers
C) all real numbers except 
D) all real numbers except 
E) all real numbers except

Accepted Answer

The domain of a function is the set of all possible input values for which the function is defined. In this case, the given value "11eb11e8_19b8_fa21_ad38_1d3379f5c3c7_TB4588_11" does not provide any information about the nature of the function or the type of values it can accept as input. Therefore, the domain is assumed to be all real numbers, unless there is any restriction or condition mentioned explicitly. None of the given answer choices provide any such restriction or condition, except for some random values in the name of the input, which do not affect the domain. Hence, B is the best choice.

Question 17

Determine the domain of  .
A) all real numbers except 
B) all real numbers
C) all real numbers except 
D) all real numbers except 
E) all real numbers except

Accepted Answer

The answer of Determine the domain of  .
A) all...

Question 18

Which of the following is the graph of the given equation? 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which of the following is the graph...

Question 19

Find the domain of  .
A) all real numbers except 
B) all real numbers
C) all real numbers except 
D) all real numbers except 
E) all real numbers except

Accepted Answer

The given expression suggests that it is a random string of characters without any mathematical significance. Therefore, the domain can be assumed to be all real numbers, unless there is a specific reason to exclude any value. Option C excludes a specific value (11eb11e8_19b7_9b4e_ad38_abf42a310859_TB4588_11), which suggests that there might be a reason to exclude it from the domain. Therefore, option C is the best choice.

Question 20

Determine the domain of the function  .
A) Domain: all real numbers except 
B) Domain: all real numbers except 
C) Domain: all real numbers except 
D) Domain: all real numbers except 
E) Domain: all real numbers

Accepted Answer

The domain of the function is not specified, so it is assumed to be all real numbers by default.

Quiz 5: Rational Functions and Conics

Determine the equations of any horizontal and vertical asymptotes of .

Given : a. Determine the domains of . b. Simplify and find any vertical asymptotes. c. Complete the table. d. Explain how the two functions differ.

Given : a. Determine the domains of . b. Simplify and find any vertical asymptotes. c. Complete the table. d. Explain how the two functions differ.

Find the domain of .

Find the domain of .

Determine the equations of any horizontal and vertical asymptotes of .

Determine the zeros (if any) of the rational function .

Determine the zeros (if any) of the rational function .

Determine the equations of the vertical and horizontal asymptotes of the graph of the function .

Determine the equations of any horizontal and vertical asymptotes of .

Given : a. Determine the domains of . b. Simplify and find any vertical asymptotes. c. Complete the table. d. Explain how the two functions differ.

Determine the zeros (if any) of the rational function .

The graph of the function is shown below. Determine the vertical and horizontal asymptotes of its graph.

Determine the equations of any horizontal and vertical asymptotes of .

The graph of the function is shown below. Determine the domain.

Determine the domain of .

Determine the domain of .

Which of the following is the graph of the given equation?

Find the domain of .

Determine the domain of the function .