Question 1

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s) of
discontinuity.
-f(x) = 4x + 3

Accepted Answer

A)  discontinuous at x = -3
B)     discontinuous at x=−34	ext { discontinuous at } x = - \frac { 3 } { 4 } discontinuous at x=−43​ 
C)     discontinuous at x=34	ext { discontinuous at } x = \frac { 3 } { 4 } discontinuous at x=43​ 
D)  continuous E) B) and D)
F) None of the above

Question 2

Determine whether the function is an even function, an odd function, or neither.
- g(x) =ex3−4g ( x )  = e ^ { x ^ { 3 } } - 4g(x) =ex3−4

Accepted Answer

A)  Even
B)  Neither
C)  Odd D) A) and C)
E) All of the above

Question 3

Determine the maximum possible number of turning points for the graph of the function.
- g(x) =52x+1g ( x )  = \frac { 5 } { 2 } x + 1g(x) =25​x+1

Accepted Answer

A)  2
B)  1
C)  0
D)  3 E) B) and D)
F) None of the above C

Question 4

Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give
the equation of the asymptote if it exists.
- f(x) =15x5x2+1f ( x )  = \frac { 15 x } { 5 x ^ { 2 } + 1 }f(x) =5x2+115x​

Accepted Answer

A)  Oblique asymptote: y = 3x
B)  Horizontal asymptote: y = 0
C)  Neither D) B) and C)
E) A) and C)

Question 5

List the possible rational zeros of the function.
- f(x) =6x4+3x3−2x2+2f ( x )  = 6 x ^ { 4 } + 3 x ^ { 3 } - 2 x ^ { 2 } + 2f(x) =6x4+3x3−2x2+2

Accepted Answer

A)    ±16,±13,±12,±23,±1,±2,±3\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2 , \pm 3±61​,±31​,±21​,±32​,±1,±2,±3 
B)    ±16,±13,±12,±1,±2\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2±61​,±31​,±21​,±1,±2 
C)    ±12,±32,±1,±2,±3,±6\pm \frac { 1 } { 2 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6±21​,±23​,±1,±2,±3,±6 
D)    ±16,±13,±12,±23,±1,±2\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2±61​,±31​,±21​,±32​,±1,±2E) C) and D)
F) A) and B)

Question 6

Graph the polynomial function.
- f(x) =x2−2x−3f ( x )  = x ^ { 2 } - 2 x - 3f(x) =x2−2x−3

Accepted Answer

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

Question 7

Determine the minimum degree of the polynomial function graphed.
- f(x) =(x−5) 2(x−3) f ( x )  = ( x - 5 )  ^ { 2 } ( x - 3 ) f(x) =(x−5) 2(x−3)

Accepted Answer

A)   
B)   
C)   
D)    E) A) and B)
F) All of the above

Question 8

Determine the minimum degree of the polynomial function graphed.
- f(x) =(x−2) (x−1) (x+1) f ( x )  = ( x - 2 )  ( x - 1 )  ( x + 1 ) f(x) =(x−2) (x−1) (x+1)

Accepted Answer

A)   
B)   
C)   
D)    E) None of the above
F) B) and C) D

Question 9

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph
the function.
- f(x) =7x6−6x5+x4+3.5x−5f ( x )  = 7 x ^ { 6 } - 6 x ^ { 5 } + x ^ { 4 } + 3.5 x - 5f(x) =7x6−6x5+x4+3.5x−5

Accepted Answer

A)  maximum number of x-intercepts: 5; minimum number of x-intercepts: 2
B)  maximum number of x-intercepts: 5; minimum number of x-intercepts: 0
C)  maximum number of x-intercepts: 6; minimum number of x-intercepts: 0
D)  maximum number of x-intercepts: 6; minimum number of x-intercepts: 2 E) A) and B)
F) None of the above D

Question 10

Find the real zeros of the function, state their multiplicities if it is a number other than 1.
- f(x) =(x+13) 2(x−2) 3f ( x )  = \left( x + \frac { 1 } { 3 } \right)  ^ { 2 } ( x - 2 )  ^ { 3 }f(x) =(x+31​) 2(x−2) 3

Accepted Answer

A)    x=−13x = - \frac { 1 } { 3 }x=−31​ , multiplicity: 2 x=2x = 2x=2 , multiplicity: 3
B)    x=13x = \frac { 1 } { 3 }x=31​ , multiplicity: 2 x=−2x = - 2x=−2 , multiplicity: 3
C)    x=−13x = - \frac { 1 } { 3 }x=−31​ , multiplicity: 2 x=2x = 2x=2 , multiplicity: 2
D)    x=13x = \frac { 1 } { 3 }x=31​ , multiplicity: 2 x=2x = 2x=2 , multiplicity: 3 E) A) and D)
F) A) and B)

Question 11

Determine whether the function is an even function, an odd function, or neither.
- f(x) =−3x5+x3f ( x )  = - 3 x ^ { 5 } + x ^ { 3 }f(x) =−3x5+x3

Accepted Answer

A)  Even
B)  Neither
C)  Odd D) All of the above
E) B) and C)

Question 12

Determine the maximum possible number of turning points for the graph of the function.
- f(x) =(x−2) (x+3) (x−5) (x−1) f ( x )  = ( x - 2 )  ( x + 3 )  ( x - 5 )  ( x - 1 ) f(x) =(x−2) (x+3) (x−5) (x−1)

Accepted Answer

A)  3
B)  1
C)  4
D)  0 E) None of the above
F) All of the above

Question 13

Determine the maximum possible number of turning points for the graph of the function.
- f(x) =−x2−4x−21f ( x )  = - x ^ { 2 } - 4 x - 21f(x) =−x2−4x−21

Accepted Answer

A)  0
B)  1
C)  3
D)  2 E) All of the above
F) A) and B)

Question 14

Determine the maximum possible number of turning points for the graph of the function.
- f(x) =x2(x2−3) (4x+1) f ( x )  = x ^ { 2 } \left( x ^ { 2 } - 3 \right)  ( 4 x + 1 ) f(x) =x2(x2−3) (4x+1)

Accepted Answer

A)  4
B)  16
C)  5
D)  2 E) None of the above
F) B) and D)

Question 15

Graph the polynomial function.
- f(x) =x4+12x3+49x2+78x+40f ( x )  = x ^ { 4 } + 12 x ^ { 3 } + 49 x ^ { 2 } + 78 x + 40f(x) =x4+12x3+49x2+78x+40

Accepted Answer

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

Question 16

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
- f(x) =x−1x2−1f ( x )  = \frac { x - 1 } { x ^ { 2 } - 1 }f(x) =x2−1x−1​

Accepted Answer

A)  -1: hole; 1: vertical asymptote
B)  1: hole; -1: vertical asymptote
C)  -1: vertical asymptote
D)  1: vertical asymptote E) B) and C)
F) A) and D)

Question 17

Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give
the equation of the asymptote if it exists.
- f(x) =5x2+20x+30x−4f ( x )  = \frac { 5 x ^ { 2 } + 20 x + 30 } { x - 4 }f(x) =x−45x2+20x+30​

Accepted Answer

A)  Horizontal asymptote: y = 5
B)  Oblique asymptote: y = 5x + 40
C)  Neither D) A) and B)
E) B) and C)

Question 18

Determine the minimum degree of the polynomial function graphed.
-

Accepted Answer

A)  4
B)  2
C)  -3
D)  3E) A) and B)
F) All of the above

Question 19

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph
the function.
- f(x) =x2−3x−3f ( x )  = x ^ { 2 } - 3 x - 3f(x) =x2−3x−3

Accepted Answer

A)  maximum number of x-intercepts: 2; minimum number of x-intercepts: 1
B)  maximum number of x-intercepts: 3; minimum number of x-intercepts: 3
C)  maximum number of x-intercepts: 2; minimum number of x-intercepts: 2
D)  maximum number of x-intercepts: 3; minimum number of x-intercepts: 2 E) A) and B)
F) A) and C)

Question 20

Describe the location, either above the x-axis or below the x-axis, of the graph of the function for large positive values of
x and for large negative values of x.
- f(x) =−9x3f ( x )  = - 9 x ^ { 3 }f(x) =−9x3

Accepted Answer

A)   large positive values of x: above x-axis , large negative values of x: above x-axis
B)  llarge positive values of x: below x-axis , large negative values of x: above x-axis
C)  large positive values of x: above x-axis , large negative values of x: below x-axis
D)  large positive values of x: below x-axis , large negative values of x: below x-axis E) C) and D)
F) A) and D)

Exam 10: Characteristics of Functions and Their Graphs

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s) of discontinuity. -f(x) = 4x + 3

Correct AnswerverifiedShow Answer

Determine whether the function is an even function, an odd function, or neither. - g(x) =ex3−4g ( x ) = e ^ { x ^ { 3 } } - 4g(x) =ex3−4

Correct AnswerverifiedShow Answer

Determine the maximum possible number of turning points for the graph of the function. - g(x) =52x+1g ( x ) = \frac { 5 } { 2 } x + 1g(x) =25​x+1

Correct AnswerverifiedC

Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give the equation of the asymptote if it exists. - f(x) =15x5x2+1f ( x ) = \frac { 15 x } { 5 x ^ { 2 } + 1 }f(x) =5x2+115x​

Correct AnswerverifiedShow Answer

List the possible rational zeros of the function. - f(x) =6x4+3x3−2x2+2f ( x ) = 6 x ^ { 4 } + 3 x ^ { 3 } - 2 x ^ { 2 } + 2f(x) =6x4+3x3−2x2+2

Correct AnswerverifiedShow Answer

Graph the polynomial function. - f(x) =x2−2x−3f ( x ) = x ^ { 2 } - 2 x - 3f(x) =x2−2x−3

Correct AnswerverifiedShow Answer

Determine the minimum degree of the polynomial function graphed. - f(x) =(x−5) 2(x−3) f ( x ) = ( x - 5 ) ^ { 2 } ( x - 3 ) f(x) =(x−5) 2(x−3)

Correct AnswerverifiedShow Answer

Determine the minimum degree of the polynomial function graphed. - f(x) =(x−2) (x−1) (x+1) f ( x ) = ( x - 2 ) ( x - 1 ) ( x + 1 ) f(x) =(x−2) (x−1) (x+1)

Correct AnswerverifiedD

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - f(x) =7x6−6x5+x4+3.5x−5f ( x ) = 7 x ^ { 6 } - 6 x ^ { 5 } + x ^ { 4 } + 3.5 x - 5f(x) =7x6−6x5+x4+3.5x−5

Correct AnswerverifiedD

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - f(x) =(x+13) 2(x−2) 3f ( x ) = \left( x + \frac { 1 } { 3 } \right) ^ { 2 } ( x - 2 ) ^ { 3 }f(x) =(x+31​) 2(x−2) 3

Correct AnswerverifiedShow Answer

Determine whether the function is an even function, an odd function, or neither. - f(x) =−3x5+x3f ( x ) = - 3 x ^ { 5 } + x ^ { 3 }f(x) =−3x5+x3

Correct AnswerverifiedShow Answer

Determine the maximum possible number of turning points for the graph of the function. - f(x) =(x−2) (x+3) (x−5) (x−1) f ( x ) = ( x - 2 ) ( x + 3 ) ( x - 5 ) ( x - 1 ) f(x) =(x−2) (x+3) (x−5) (x−1)

Correct AnswerverifiedShow Answer

Determine the maximum possible number of turning points for the graph of the function. - f(x) =−x2−4x−21f ( x ) = - x ^ { 2 } - 4 x - 21f(x) =−x2−4x−21

Correct AnswerverifiedShow Answer

Determine the maximum possible number of turning points for the graph of the function. - f(x) =x2(x2−3) (4x+1) f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 3 \right) ( 4 x + 1 ) f(x) =x2(x2−3) (4x+1)

Correct AnswerverifiedShow Answer

Graph the polynomial function. - f(x) =x4+12x3+49x2+78x+40f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 49 x ^ { 2 } + 78 x + 40f(x) =x4+12x3+49x2+78x+40

Correct AnswerverifiedShow Answer

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - f(x) =x−1x2−1f ( x ) = \frac { x - 1 } { x ^ { 2 } - 1 }f(x) =x2−1x−1​

Correct AnswerverifiedShow Answer

Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give the equation of the asymptote if it exists. - f(x) =5x2+20x+30x−4f ( x ) = \frac { 5 x ^ { 2 } + 20 x + 30 } { x - 4 }f(x) =x−45x2+20x+30​

Correct AnswerverifiedShow Answer

Determine the minimum degree of the polynomial function graphed. -

Correct AnswerverifiedShow Answer

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - f(x) =x2−3x−3f ( x ) = x ^ { 2 } - 3 x - 3f(x) =x2−3x−3

Correct AnswerverifiedShow Answer

Describe the location, either above the x-axis or below the x-axis, of the graph of the function for large positive values of x and for large negative values of x. - f(x) =−9x3f ( x ) = - 9 x ^ { 3 }f(x) =−9x3

Correct AnswerverifiedShow Answer

Correct Answer
verified

Determine whether the function is an even function, an odd function, or neither. - $g ( x ) = e ^ { x ^ { 3 } } - 4$

Correct Answer
verified

Determine the maximum possible number of turning points for the graph of the function. - $g ( x ) = \frac { 5 } { 2 } x + 1$

Correct Answer
verified
C

Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give the equation of the asymptote if it exists. - $f ( x ) = \frac { 15 x } { 5 x ^ { 2 } + 1 }$

Correct Answer
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List the possible rational zeros of the function. - $f ( x ) = 6 x ^ { 4 } + 3 x ^ { 3 } - 2 x ^ { 2 } + 2$

Correct Answer
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Graph the polynomial function. - $f ( x ) = x ^ { 2 } - 2 x - 3$ $Graph the polynomial function. - f ( x ) = x ^ { 2 } - 2 x - 3 A) B) C) D)$

Correct Answer
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Determine the minimum degree of the polynomial function graphed. - $f ( x ) = ( x - 5 ) ^ { 2 } ( x - 3 )$ $Determine the minimum degree of the polynomial function graphed. - f ( x ) = ( x - 5 ) ^ { 2 } ( x - 3 ) A) B) C) D)$

Correct Answer
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Determine the minimum degree of the polynomial function graphed. - $f ( x ) = ( x - 2 ) ( x - 1 ) ( x + 1 )$

Correct Answer
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D

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - $f ( x ) = 7 x ^ { 6 } - 6 x ^ { 5 } + x ^ { 4 } + 3.5 x - 5$

Correct Answer
verified
D

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = \left( x + \frac { 1 } { 3 } \right) ^ { 2 } ( x - 2 ) ^ { 3 }$

Correct Answer
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Determine whether the function is an even function, an odd function, or neither. - $f ( x ) = - 3 x ^ { 5 } + x ^ { 3 }$

Correct Answer
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Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = ( x - 2 ) ( x + 3 ) ( x - 5 ) ( x - 1 )$

Correct Answer
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Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = - x ^ { 2 } - 4 x - 21$

Correct Answer
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Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 3 \right) ( 4 x + 1 )$

Correct Answer
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Graph the polynomial function. - $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 49 x ^ { 2 } + 78 x + 40$ $Graph the polynomial function. - f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 49 x ^ { 2 } + 78 x + 40 A) B) C) D)$

Correct Answer
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Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } - 1 }$

Correct Answer
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Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give the equation of the asymptote if it exists. - $f ( x ) = \frac { 5 x ^ { 2 } + 20 x + 30 } { x - 4 }$

Correct Answer
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Correct Answer
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Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - $f ( x ) = x ^ { 2 } - 3 x - 3$

Correct Answer
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Describe the location, either above the x-axis or below the x-axis, of the graph of the function for large positive values of x and for large negative values of x. - $f ( x ) = - 9 x ^ { 3 }$

Correct Answer
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