Question 1

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) =−2x−54x−3f ( x )  = \frac { - 2 x - 5 } { 4 x - 3 }f(x) =4x−3−2x−5​

Accepted Answer

A)     Horizontal asymptote: y=−12	ext { Horizontal asymptote: } \mathrm { y } = - \frac { 1 } { 2 } Horizontal asymptote: y=−21​ 
B)     Oblique asymptote: y=−12x−5	ext { Oblique asymptote: } y = - \frac { 1 } { 2 } x - 5 Oblique asymptote: y=−21​x−5 
C)  Neither

Question 2

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

Accepted Answer

A)   
B)   
C)    
D)

Question 3

Find all the rational zeros of the function.
- f(x) =x5−3x4−5x3+15x2+4x−12f ( x )  = x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + 15 x ^ { 2 } + 4 x - 12f(x) =x5−3x4−5x3+15x2+4x−12

Accepted Answer

A)  -1, -2, -3
B)  1, -1, 2, -2, -3
C)  1, -1, 2, -2, 3
D)  1, 2, 3

Question 4

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s) of
discontinuity.
- f(x) =7(x−6) 2f ( x )  = 7 ( x - 6 )  ^ { 2 }f(x) =7(x−6) 2

Accepted Answer

A)  continuous
B)  discontinuous at x = 6
C)     discontinuous at x=67	ext { discontinuous at } x = \frac { 6 } { 7 } discontinuous at x=76​ 
D)  discontinuous at x = -6

Question 5

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial
function.
- f(x) =−5x7+x3−x2+4f ( x )  = - 5 x ^ { 7 } + x ^ { 3 } - x ^ { 2 } + 4f(x) =−5x7+x3−x2+4

Accepted Answer

A)  2 or 0 positive zeros, 3 or 1 negative zeros
B)  3 or 1 positive zeros, 2 or 0 negative zeros
C)  2 or 0 positive zeros, 2 or 0 negative zeros
D)  3 or 1 positive zeros, 3 or 1 negative zeros

Question 6

Use the Boundedness Theorem to determine if the zeros of f(x) are bounded over the given interval. If this cannot be
determined, indicate so.
- f(x) =x4−3x3+5x2−9x−8 in [−1,4]f ( x )  = x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } - 9 x - 8 	ext { in } [ - 1,4 ]f(x) =x4−3x3+5x2−9x−8 in [−1,4]

Accepted Answer

A)  Cannot determine
B)  Yes

Question 7

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
- f(x) =x2−4x−5x+1f ( x )  = \frac { x ^ { 2 } - 4 x - 5 } { x + 1 }f(x) =x+1x2−4x−5​

Accepted Answer

A)  -1: hole
B)  1: hole
C)  1: vertical asymptote
D)  -1: vertical asymptote

Question 8

Find all real zeros (estimate the irrational zeros to the nearest hundredth) .
- f(x) =x4−3x2−10f ( x )  = x ^ { 4 } - 3 x ^ { 2 } - 10f(x) =x4−3x2−10

Accepted Answer

A)  -2.24, 2.24
B)  5, -1.41, 1.41
C)  3.16, -5
D)  10, 2.24

Question 9

Determine the minimum degree of the polynomial function graphed.
- f(x) =x4−5x3+4x2f ( x )  = x ^ { 4 } - 5 x ^ { 3 } + 4 x ^ { 2 }f(x) =x4−5x3+4x2

Accepted Answer

A)   
B)   
C)   
D)

Question 10

Determine the minimum degree of the polynomial function graphed.
-

Accepted Answer

A)  2
B)  3
C)  4
D)  -4

Question 11

Classify the function as continuous or discontinuous.
-

Accepted Answer

A)  continuous
B)  discontinuous

Question 12

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial
function.
- f(x) =x4−10f ( x )  = x ^ { 4 } - 10f(x) =x4−10

Accepted Answer

A)  1 positive zero, 1 negative zero
B)  0 positive zeros, 0 negative zeros
C)  1 positive zero, 0 negative zeros
D)  0 positive zeros, 1 negative zero

Question 13

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
- f(x) =x+7x2+2x−35f ( x )  = \frac { x + 7 } { x ^ { 2 } + 2 x - 35 }f(x) =x2+2x−35x+7​

Accepted Answer

A)  -7: hole; 5: vertical asymptote
B)  5: vertical asymptote
C)  -5: vertical asymptote
D)  7: hole; -5: vertical asymptote

Question 14

Find the x-intercepts of the function.
- f(x) =x2−18x+81f ( x )  = x ^ { 2 } - 18 x + 81f(x) =x2−18x+81

Accepted Answer

A)  x-intercept: (9, 0) 
B)  x-intercept: (-9, 0) 
C)  x-intercept: (18, 0) 
D)  x-intercept: (9, 0) , x-intercept: (-9, 0)

Question 15

Classify the function as continuous or discontinuous.
-

Accepted Answer

A)  discontinuous
B)  continuous

Question 16

Classify the function as continuous or discontinuous.
-

Accepted Answer

A)  discontinuous
B)  continuous

Question 17

Graph the greatest integer function.
- f(x) =⟦x+43⟧f ( x )  = \llbracket \frac { x + 4 } { 3 } \rrbracketf(x) =[[3x+4​]]

Accepted Answer

A)   
B)   
C)   
D)

Question 18

List the possible rational zeros of the function.
- x5−3x2+2x+10x ^ { 5 } - 3 x ^ { 2 } + 2 x + 10x5−3x2+2x+10

Accepted Answer

A)    ±1,±15,±12,±110,±5,±2,±10\pm 1 , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 10 } , \pm 5 , \pm 2 , \pm 10±1,±51​,±21​,±101​,±5,±2,±10 
B)    ±1,±5,±2\pm 1 , \pm 5 , \pm 2±1,±5,±2 
C)    ±1,±5,±2,±10\pm 1 , \pm 5 , \pm 2 , \pm 10±1,±5,±2,±10 
D)    ±1,±15,±12,±110\pm 1 , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 10 }±1,±51​,±21​,±101​

Question 19

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial
function.
- f(x) =x5+x4+x2+x+7f ( x )  = x ^ { 5 } + x ^ { 4 } + x ^ { 2 } + x + 7f(x) =x5+x4+x2+x+7

Accepted Answer

A)  0 positive zeros, 1 negative zero
B)  0 positive zeros, 0 negative zeros
C)  0 positive zeros, 2 or 0 negative zeros
D)  0 positive zeros, 3 or 1 negative zeros

Question 20

Determine the maximum possible number of turning points for the graph of the function.
- f(x) =(7x−2) 2(x2−1) (x+1) f ( x )  = ( 7 x - 2 )  ^ { 2 } \left( x ^ { 2 } - 1 \right)  ( x + 1 ) f(x) =(7x−2) 2(x2−1) (x+1)

Accepted Answer

A)  4
B)  2
C)  5
D)  35

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) =7(x−6) 2f ( x ) = 7 ( x - 6 ) ^ { 2 }f(x) =7(x−6) 2

Correct AnswerverifiedShow Answer

Graph the greatest integer function. - f(x) =⟦x+43⟧f ( x ) = \llbracket \frac { x + 4 } { 3 } \rrbracketf(x) =[[3x+4​]]

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Determine the minimum degree of the polynomial function graphed. -

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Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - f(x) =x4−10f ( x ) = x ^ { 4 } - 10f(x) =x4−10

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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) =−2x−54x−3f ( x ) = \frac { - 2 x - 5 } { 4 x - 3 }f(x) =4x−3−2x−5​

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+7x2+2x−35f ( x ) = \frac { x + 7 } { x ^ { 2 } + 2 x - 35 }f(x) =x2+2x−35x+7​

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Find all real zeros (estimate the irrational zeros to the nearest hundredth) . - f(x) =x4−3x2−10f ( x ) = x ^ { 4 } - 3 x ^ { 2 } - 10f(x) =x4−3x2−10

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Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - f(x) =−5x7+x3−x2+4f ( x ) = - 5 x ^ { 7 } + x ^ { 3 } - x ^ { 2 } + 4f(x) =−5x7+x3−x2+4

Correct AnswerverifiedShow Answer

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

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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) =x2−4x−5x+1f ( x ) = \frac { x ^ { 2 } - 4 x - 5 } { x + 1 }f(x) =x+1x2−4x−5​

Correct AnswerverifiedShow Answer

Determine the minimum degree of the polynomial function graphed. - f(x) =x4−5x3+4x2f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 4 x ^ { 2 }f(x) =x4−5x3+4x2

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Classify the function as continuous or discontinuous. -

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Classify the function as continuous or discontinuous. -

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List the possible rational zeros of the function. - x5−3x2+2x+10x ^ { 5 } - 3 x ^ { 2 } + 2 x + 10x5−3x2+2x+10

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Find the x-intercepts of the function. - f(x) =x2−18x+81f ( x ) = x ^ { 2 } - 18 x + 81f(x) =x2−18x+81

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Find all the rational zeros of the function. - f(x) =x5−3x4−5x3+15x2+4x−12f ( x ) = x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + 15 x ^ { 2 } + 4 x - 12f(x) =x5−3x4−5x3+15x2+4x−12

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Determine the maximum possible number of turning points for the graph of the function. - f(x) =(7x−2) 2(x2−1) (x+1) f ( x ) = ( 7 x - 2 ) ^ { 2 } \left( x ^ { 2 } - 1 \right) ( x + 1 ) f(x) =(7x−2) 2(x2−1) (x+1)

Correct AnswerverifiedShow Answer

Classify the function as continuous or discontinuous. -

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Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - f(x) =x5+x4+x2+x+7f ( x ) = x ^ { 5 } + x ^ { 4 } + x ^ { 2 } + x + 7f(x) =x5+x4+x2+x+7

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s) of discontinuity. - $f ( x ) = 7 ( x - 6 ) ^ { 2 }$

Correct Answer
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Graph the greatest integer function. - $f ( x ) = \llbracket \frac { x + 4 } { 3 } \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket \frac { x + 4 } { 3 } \rrbracket A) B) C) D)$

Correct Answer
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Correct Answer
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Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - $f ( x ) = x ^ { 4 } - 10$

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. - $f ( x ) = \frac { - 2 x - 5 } { 4 x - 3 }$

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. - $f ( x ) = \frac { x + 7 } { x ^ { 2 } + 2 x - 35 }$

Correct Answer
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Find all real zeros (estimate the irrational zeros to the nearest hundredth) . - $f ( x ) = x ^ { 4 } - 3 x ^ { 2 } - 10$

Correct Answer
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Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - $f ( x ) = - 5 x ^ { 7 } + x ^ { 3 } - x ^ { 2 } + 4$

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

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. - $f ( x ) = \frac { x ^ { 2 } - 4 x - 5 } { x + 1 }$

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Determine the minimum degree of the polynomial function graphed. - $f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 4 x ^ { 2 }$ $Determine the minimum degree of the polynomial function graphed. - f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 4 x ^ { 2 } A) B) C) D)$

Correct Answer
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Correct Answer
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Correct Answer
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List the possible rational zeros of the function. - $x ^ { 5 } - 3 x ^ { 2 } + 2 x + 10$

Correct Answer
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Find the x-intercepts of the function. - $f ( x ) = x ^ { 2 } - 18 x + 81$

Correct Answer
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Find all the rational zeros of the function. - $f ( x ) = x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + 15 x ^ { 2 } + 4 x - 12$

Correct Answer
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Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = ( 7 x - 2 ) ^ { 2 } \left( x ^ { 2 } - 1 \right) ( x + 1 )$

Correct Answer
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Correct Answer
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Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - $f ( x ) = x ^ { 5 } + x ^ { 4 } + x ^ { 2 } + x + 7$

Correct Answer
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Correct Answer
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