Question 1

Find the domain of the function and identify any vertical and horizontal asymptotes.​  f(x) =x+4x2−16f ( x )  = \frac { x + 4 } { x ^ { 2 } - 16 }f(x) =x2−16x+4​  ​

Accepted Answer

A)  The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0.
B)  The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = -16,and a horizontal asymptote at y = 0.
C)  The domain is all real numbers x except x = ±16.There is a vertical asymptote at x = -16,and a horizontal asymptote at y = 0.
D)  The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = 4,and a horizontal asymptote at y = 0.
E)  The domain is all real numbers x except x = ±16.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0. F) D) and E)
G) A) and B)

Question 2

Given  f(x) =x2−4x+3x−7f ( x )  = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }f(x) =x−7x2−4x+3​  ,determine the equations of any slant and vertical asymptote.

Accepted Answer

A)  slant: y = x - 3;vertical: x = 3
B)  slant: y = x + 3;vertical: x = 7
C)  slant: none;vertical: none
D)  slant: y = x - 11;vertical: none
E)  slant: y = x + 10;vertical: x = -4 F) B) and D)
G) A) and C)

Question 3

Find the domain of the function and identify any vertical and horizontal asymptotes.​  f(x) =7+x7−xf ( x )  = \frac { 7 + x } { 7 - x }f(x) =7−x7+x​  ​

Accepted Answer

A)  Domain: all real numbers x except x = 7 Vertical asymptote: x = 7Horizontal asymptote: y = -1
B)  Domain: all real numbers x Vertical asymptote: x = -7Horizontal asymptote: y = 0
C)  Domain: all real numbers x except x = 0 Vertical asymptote: x = 0Horizontal asymptote: y = -1
D)  Domain: all real numbers x except x = 7 Vertical asymptote: x = 0Horizontal asymptote: y = -7
E)  Domain: all real numbers x except x = -7 Vertical asymptote: x = 0Horizontal asymptote: y = 7 F) B) and D)
G) A) and E)

Question 4

Find the domain of  f(x) =x−7x2−49f ( x )  = \frac { x - 7 } { x ^ { 2 } - 49 }f(x) =x2−49x−7​  .

Accepted Answer

A)  all real numbers except x = -7
B)  all real numbers except x = 49
C)  all real numbers except x = 7
D)  all real numbers except x = 7 and x = -7
E)  all real numbers F) A) and E)
G) B) and E)

Question 5

Determine the zeros (if any) of the rational function  g(x) =5+4x2+5g ( x )  = 5 + \frac { 4 } { x ^ { 2 } + 5 }g(x) =5+x2+54​  .

Accepted Answer

A)    x=−5,x=5x = - \sqrt { 5 } , x = \sqrt { 5 }x=−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​,x=5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)  x = -4
C)    x=−45,x=45x = - \frac { 4 } { 5 } , x = \frac { 4 } { 5 }x=−54​,x=54​ 
D)  x = -5,x = 5
E)  no zeros F) A) and B)
G) None of the above

Question 6

Find domain of the following function.  g(x) =x2−49x2−6x−7g ( x )  = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }g(x) =x2−6x−7x2−49​  ​

Accepted Answer

A)  all real numbers x except x = -49 and x = -1
B)  all real numbers x except x = -6 and x = ​7
C)  all real numbers x except x = 6 and x = 49
D)  all real numbers x except x = 7 and x = -1
E)  all real numbers x except x = -7 and x = 1 F) A) and E)
G) A) and C)

Question 7

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by​  N=24(5+3t) 1+0.04t,t≥0N = \frac { 24 ( 5 + 3 t )  } { 1 + 0.04 t } , t \geq 0N=1+0.04t24(5+3t) ​,t≥0  ​ where t is the time in years.Find the populations when t = 40.
(Round your answer to the nearest whole number. ) 
​

Accepted Answer

A)  1,154 deer
B)  1,306 deer
C)  1,275 deer
D)  1,240 deer
E)  1,200 deer F) B) and D)
G) B) and C)

Question 8

Find the domain of the function. ​​  g(s) =−3ss−9g ( s )  = \frac { - 3 s } { s - 9 }g(s) =s−9−3s​  ​

Accepted Answer

A)  s = 9
B)  all real numbers s ≠ 9,s ≠ 0
C)  ​s = 9,s = 0
D)  all real numbers s ≠ 9
E)    ∅\varnothing∅F) B) and D)
G) B) and E)

Question 9

Select the correct graph of the function  f(x) =6x+4f ( x )  = \frac { 6 } { x + 4 }f(x) =x+46​  . ​

Accepted Answer

A)  ​ 
B)  ​ 
C)  ​ 
D)  ​ 
E)  ​  F) A) and C)
G) C) and D)

Question 10

Determine the value that the function f approaches as the magnitude of x increases.​  f(x) =2−4xf ( x )  = 2 - \frac { 4 } { x }f(x) =2−x4​  ​

Accepted Answer

A)  1
B)  -4
C)  2
D)  -2
E)  -1.75 F) A) and E)
G) A) and D)

Question 11

Find the zeros of the rational function.​  f(x) =1−5x−10f ( x )  = 1 - \frac { 5 } { x - 10 }f(x) =1−x−105​  ​

Accepted Answer

A)  x = -15
B)  x = -5
C)  x = 15
D)  x = -10
E)  x = 5 F) A) and B)
G) All of the above

Question 12

Find the domain of the function and identify any vertical and horizontal asymptotes.​  f(x) =5x2+8x2+x+9f ( x )  = \frac { 5 x ^ { 2 } + 8 } { x ^ { 2 } + x + 9 }f(x) =x2+x+95x2+8​  ​

Accepted Answer

A)  Domain: all real numbers x Vertical asymptote: No vertical asymptoteHorizontal asymptote: y = 5
B)  Domain: all real numbers except x = 0 Vertical asymptote: x = 0Horizontal asymptote: y = -8
C)  Domain: all real numbers x Vertical asymptote: x = -5Horizontal asymptote: y = 0
D)  Domain: all real numbers except x = 5 Vertical asymptote: No vertical asymptoteHorizontal asymptote: No horizontal asymptote
E)  Domain: all real numbers except x = 9 Vertical asymptote: x = 5Horizontal asymptote: y = 8 F) A) and E)
G) A) and C)

Question 13

Determine the equations of any horizontal and vertical asymptotes of  f(x) =2x2−x−9x2+3x+3f ( x )  = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }f(x) =x2+3x+32x2−x−9​  .

Accepted Answer

A)  horizontal: y = 4;vertical: x = 0
B)  horizontal: y = - 3;vertical: x = -4
C)  horizontal: y = 2;vertical: none
D)  horizontal: y = 1;vertical: x = - 3
E)  horizontal: y = -2;vertical: x = 3 and x = -4 F) C) and E)
G) A) and E)

Question 14

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by​  C=235p100−p,0≤p≤100C = \frac { 235 p } { 100 - p } , 0 \leq p \leq 100C=100−p235p​,0≤p≤100  .
​
Find the costs of removing 70% of the pollutants.
(Round your answer to two decimal places. ) 
​

Accepted Answer

A)  $568.33 million
B)  $588.33 million
C)  $578.33 million
D)  $558.33 million
E)  $548.33 million F) A) and B)
G) A) and E)

Question 15

Select the correct graph of the following function.​  f(x) =x2+6xf ( x )  = \frac { x ^ { 2 } + 6 } { x }f(x) =xx2+6​  ​

Accepted Answer

A)  ​ 
B)  ​ 
C)  ​ 
D)  ​ 
E)  ​  F) B) and D)
G) B) and E)

Question 16

Find the domain of  f(x) =x2−16x2+4x−32f ( x )  = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }f(x) =x2+4x−32x2−16​  .

Accepted Answer

A)  all real numbers except x = 8 and x = -4
B)  all real numbers
C)  all real numbers except x = 4 and x = -8
D)  all real numbers except x = -4,x = 4 and x = -8
E)  all real numbers except x = -8 F) A) and B)
G) A) and C)

Question 17

Find domain of the following function.​  g(x) =1−9x1−xg ( x )  = \frac { 1 - 9 x } { 1 - x }g(x) =1−x1−9x​  ​

Accepted Answer

A)  all real numbers x
B)  all real numbers x except x = 1
C)  all real numbers x except x = -9
D)  all real numbers x except x = -1
E)  all real numbers x except x = 9 F) A) and B)
G) C) and D)

Question 18

The graph of the function ​​  f(x) =3xx2−4f ( x )  = \frac { 3 x } { x ^ { 2 } - 4 }f(x) =x2−43x​  is shown below.Determine the domain.

Accepted Answer

A)  Domain: all real numbers except x = -2 and x = 2
B)  Domain: all real numbers except x = 2
C)  Domain: all real numbers except x = 0
D)  Domain: all real numbers except x = 4 E) None of the above
F) B) and D)

Question 19

Which of the following is the graph of the given equation?​  f(x) =2−xx+3f ( x )  = \frac { 2 - x } { x + 3 }f(x) =x+32−x​  ​

Accepted Answer

A)   
B)   
C)   
D)  ​ 
E)    F) A) and E)
G) C) and D)

Question 20

Determine the equations of any horizontal and vertical asymptotes of  f(x) =x2x2+4f ( x )  = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }f(x) =x2+4x2​  .

Accepted Answer

A)  horizontal: y = 2;vertical: x = -2
B)  horizontal: x = 1;vertical: none
C)  horizontal: none;vertical: none
D)  horizontal: y = 1;vertical: none
E)  horizontal: y = -2;vertical: x = 1 F) A) and C)
G) C) and D)

Exam 16: Rational Functions

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$ .

Correct Answer
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Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } + 6 } { x }$

Correct Answer
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Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = 2 - \frac { 4 } { x }$

Correct Answer
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Find the domain of $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 49 }$ .

Correct Answer
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Correct Answer
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Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }$

Correct Answer
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Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$

Correct Answer
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Given $f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }$ ,determine the equations of any slant and vertical asymptote.

Correct Answer
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Find domain of the following function. $g ( x ) = \frac { 1 - 9 x } { 1 - x }$

Correct Answer
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Find the zeros of the rational function. $f ( x ) = 1 - \frac { 5 } { x - 10 }$

Correct Answer
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Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x + 4 } { x ^ { 2 } - 16 }$

Correct Answer
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Find the domain of the function. $g ( s ) = \frac { - 3 s } { s - 9 }$

Correct Answer
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Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 7 + x } { 7 - x }$

Correct Answer
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Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 5 x ^ { 2 } + 8 } { x ^ { 2 } + x + 9 }$

Correct Answer
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Select the correct graph of the function $f ( x ) = \frac { 6 } { x + 4 }$ .

Correct Answer
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Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }$ .

Correct Answer
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Find the domain of $f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }$ .

Correct Answer
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The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by $C = \frac { 235 p } { 100 - p } , 0 \leq p \leq 100$ . Find the costs of removing 70% of the pollutants. (Round your answer to two decimal places. )

Correct Answer
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Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }$ .

Correct Answer
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The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by $N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$ where t is the time in years.Find the populations when t = 40. (Round your answer to the nearest whole number. )

Correct Answer
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Exam 16: Rational Functions

Determine the zeros (if any) of the rational function g(x) =5+4x2+5g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }g(x) =5+x2+54​ .

Correct AnswerverifiedShow Answer

Select the correct graph of the following function.​ f(x) =x2+6xf ( x ) = \frac { x ^ { 2 } + 6 } { x }f(x) =xx2+6​ ​

Correct AnswerverifiedShow Answer

Determine the value that the function f approaches as the magnitude of x increases.​ f(x) =2−4xf ( x ) = 2 - \frac { 4 } { x }f(x) =2−x4​ ​

Correct AnswerverifiedShow Answer

Find the domain of f(x) =x−7x2−49f ( x ) = \frac { x - 7 } { x ^ { 2 } - 49 }f(x) =x2−49x−7​ .

Correct AnswerverifiedShow Answer

The graph of the function ​​ f(x) =3xx2−4f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 }f(x) =x2−43x​ is shown below.Determine the domain.

Correct AnswerverifiedShow Answer

Find domain of the following function. g(x) =x2−49x2−6x−7g ( x ) = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }g(x) =x2−6x−7x2−49​ ​

Correct AnswerverifiedShow Answer

Which of the following is the graph of the given equation?​ f(x) =2−xx+3f ( x ) = \frac { 2 - x } { x + 3 }f(x) =x+32−x​ ​

Correct AnswerverifiedShow Answer

Given f(x) =x2−4x+3x−7f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }f(x) =x−7x2−4x+3​ ,determine the equations of any slant and vertical asymptote.

Correct AnswerverifiedShow Answer

Find domain of the following function.​ g(x) =1−9x1−xg ( x ) = \frac { 1 - 9 x } { 1 - x }g(x) =1−x1−9x​ ​

Correct AnswerverifiedShow Answer

Find the zeros of the rational function.​ f(x) =1−5x−10f ( x ) = 1 - \frac { 5 } { x - 10 }f(x) =1−x−105​ ​

Correct AnswerverifiedShow Answer

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x) =x+4x2−16f ( x ) = \frac { x + 4 } { x ^ { 2 } - 16 }f(x) =x2−16x+4​ ​

Correct AnswerverifiedShow Answer

Find the domain of the function. ​​ g(s) =−3ss−9g ( s ) = \frac { - 3 s } { s - 9 }g(s) =s−9−3s​ ​

Correct AnswerverifiedShow Answer

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x) =7+x7−xf ( x ) = \frac { 7 + x } { 7 - x }f(x) =7−x7+x​ ​

Correct AnswerverifiedShow Answer

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x) =5x2+8x2+x+9f ( x ) = \frac { 5 x ^ { 2 } + 8 } { x ^ { 2 } + x + 9 }f(x) =x2+x+95x2+8​ ​

Correct AnswerverifiedShow Answer

Select the correct graph of the function f(x) =6x+4f ( x ) = \frac { 6 } { x + 4 }f(x) =x+46​ . ​

Correct AnswerverifiedShow Answer

Determine the equations of any horizontal and vertical asymptotes of f(x) =x2x2+4f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }f(x) =x2+4x2​ .

Correct AnswerverifiedShow Answer

Find the domain of f(x) =x2−16x2+4x−32f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }f(x) =x2+4x−32x2−16​ .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Determine the equations of any horizontal and vertical asymptotes of f(x) =2x2−x−9x2+3x+3f ( x ) = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }f(x) =x2+3x+32x2−x−9​ .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Determine the zeros (if any) of the rational function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$ .

Correct Answer
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Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } + 6 } { x }$

Correct Answer
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Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = 2 - \frac { 4 } { x }$

Correct Answer
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Find the domain of $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 49 }$ .

Correct Answer
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Correct Answer
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Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }$

Correct Answer
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Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$

Correct Answer
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Given $f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }$ ,determine the equations of any slant and vertical asymptote.

Correct Answer
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Find domain of the following function. $g ( x ) = \frac { 1 - 9 x } { 1 - x }$

Correct Answer
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Find the zeros of the rational function. $f ( x ) = 1 - \frac { 5 } { x - 10 }$

Correct Answer
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Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x + 4 } { x ^ { 2 } - 16 }$

Correct Answer
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Find the domain of the function. $g ( s ) = \frac { - 3 s } { s - 9 }$

Correct Answer
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Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 7 + x } { 7 - x }$

Correct Answer
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Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 5 x ^ { 2 } + 8 } { x ^ { 2 } + x + 9 }$

Correct Answer
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Select the correct graph of the function $f ( x ) = \frac { 6 } { x + 4 }$ .

Correct Answer
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Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }$ .

Correct Answer
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Find the domain of $f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }$ .

Correct Answer
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Correct Answer
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Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }$ .

Correct Answer
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Correct Answer
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