Question 1

Find all real zeros (estimate the irrational zeros to the nearest hundredth) .
- f(x) =x3+6x2+5x+30f ( x )  = x ^ { 3 } + 6 x ^ { 2 } + 5 x + 30f(x) =x3+6x2+5x+30

Accepted Answer

A)  -6, -2.24, 2.24
B)  -6
C)  5.48, 6
D)  -30

Question 2

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point.
- g(x) =xx+5g ( x )  = \frac { x } { x + 5 }g(x) =x+5x​

Accepted Answer

A)  -5: vertical asymptote
B)  0: vertical asymptote; 5: vertical asymptote
C)  0: vertical asymptote; -5: vertical asymptote
D)  no vertical asymptotes

Question 3

Find the x-intercepts of the function.
- f(x) =x3+x2−30xf ( x )  = x ^ { 3 } + x ^ { 2 } - 30 xf(x) =x3+x2−30x

Accepted Answer

A)  x-intercept: (0, 0) , x-intercept: (- 6, 0) , x-intercept: (5, 0) 
B)  x-intercept: (4, 0) , x-intercept: (5, 0) 
C)  x-intercept: (- 6, 0) , x-intercept: (5, 0) 
D)  x-intercept: (0, 0) , x-intercept: (4, 0) , x-intercept: (5, 0)

Question 4

Graph the polynomial function.
- f(x) =x4−5x2+4f ( x )  = x ^ { 4 } - 5 x ^ { 2 } + 4f(x) =x4−5x2+4

Accepted Answer

A)   
B)   
C)   
D)

Question 5

Find all the rational zeros of the function.
- f(x) =2x3−9x2+7x+6f ( x )  = 2 x ^ { 3 } - 9 x ^ { 2 } + 7 x + 6f(x) =2x3−9x2+7x+6

Accepted Answer

A)    −32,−1,−2- \frac { 3 } { 2 } , - 1 , - 2−23​,−1,−2 
B)    −12,2,3- \frac { 1 } { 2 } , 2,3−21​,2,3 
C)    12,2,−3\frac { 1 } { 2 } , 2 , - 321​,2,−3 
D)    32,−1,2\frac { 3 } { 2 } , - 1,223​,−1,2

Question 6

Find the x-intercepts of the function.
- f(x) =(x+15) 2(x+9) 5f ( x )  = \left( x + \frac { 1 } { 5 } \right)  ^ { 2 } ( x + 9 )  ^ { 5 }f(x) =(x+51​) 2(x+9) 5

Accepted Answer

A)    x-intercept: (−15,0) ,x-intercept: (9,0) x 	ext {-intercept: } \left( - \frac { 1 } { 5 } , 0 ight)  , x 	ext {-intercept: } ( 9,0 ) x-intercept: (−51​,0) ,x-intercept: (9,0)  
B)    x-intercept: (15,0) ,x-intercept: (−9,0) x 	ext {-intercept: } \left( \frac { 1 } { 5 } , 0 ight)  , x 	ext {-intercept: } ( - 9,0 ) x-intercept: (51​,0) ,x-intercept: (−9,0)  
C)    x-intercept: (15,0) ,x-intercept: (9,0) x 	ext {-intercept: } \left( \frac { 1 } { 5 } , 0 ight)  , x 	ext {-intercept: } ( 9,0 ) x-intercept: (51​,0) ,x-intercept: (9,0)  
D)    x-intercept: (−15,0) ,x-intercept: (−9,0) \mathrm { x } 	ext {-intercept: } \left( - \frac { 1 } { 5 } , 0 ight)  , \mathrm { x } 	ext {-intercept: } ( - 9,0 ) x-intercept: (−51​,0) ,x-intercept: (−9,0)

Question 7

Graph the rational function.
- f(x) =2x(x−2) (x+4) f ( x )  = \frac { 2 x } { ( x - 2 )  ( x + 4 )  }f(x) =(x−2) (x+4) 2x​

Accepted Answer

A)   
B)   
C)   
D)

Question 8

Find all the rational zeros of the function.
- f(x) =x4+x2−2f ( x )  = x ^ { 4 } + x ^ { 2 } - 2f(x) =x4+x2−2

Accepted Answer

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

Question 9

Use the Intermediate Value Theorem to determine if a real zero of f(x) occurs in the given interval. If this cannot be
determined, indicate so.
- f(x) =2x4−7x3+4x2−x+4 in (2,3) f ( x )  = 2 x ^ { 4 } - 7 x ^ { 3 } + 4 x ^ { 2 } - x + 4 	ext { in } ( 2,3 ) f(x) =2x4−7x3+4x2−x+4 in (2,3)

Accepted Answer

A)  Cannot determine
B)  Yes

Question 10

Determine whether the function is an even function, an odd function, or neither.
- g(x) =e3x+5g ( x )  = e ^ { 3 x } + 5g(x) =e3x+5

Accepted Answer

A)  Odd
B)  Neither
C)  Even

Question 11

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) =x3+3x2+8xf ( x )  = \frac { x ^ { 3 } + 3 } { x ^ { 2 } + 8 x }f(x) =x2+8xx3+3​

Accepted Answer

A)  Oblique asymptote: y = x - 8
B)  Horizontal asymptote: y = 1
C)  Neither

Question 12

Graph the greatest integer function.
- f(x) =⟦13x⟧f ( x )  = \llbracket \frac { 1 } { 3 } x \rrbracketf(x) =[[31​x]]

Accepted Answer

A)   
B)   
C)   
D)

Question 13

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

Accepted Answer

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

Question 14

Find the real zeros of the function, state their multiplicities if it is a number other than 1.
- f(x) =x2−25f ( x )  = x ^ { 2 } - 25f(x) =x2−25

Accepted Answer

A)  x = 5, multiplicity: 2
B)    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'/>​ 
C)  x = -5, multiplicity: 2
D)  x = 5, x = -5

Question 15

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s) of
discontinuity.
- f(x) =⟦x3⟧f ( x )  = \llbracket \frac { x } { 3 } \rrbracketf(x) =[[3x​]]

Accepted Answer

A)  discontinuous at x = . . . -3, -2, -1, 0, 1, 2, 3, . . .
B)  continuous
C)     discontinuous at x=…−1,−23,−13,0,13,23,1,…	ext { discontinuous at } x = \ldots - 1 , - \frac { 2 } { 3 } , - \frac { 1 } { 3 } , 0 , \frac { 1 } { 3 } , \frac { 2 } { 3 } , 1 , \ldots discontinuous at x=…−1,−32​,−31​,0,31​,32​,1,… 
D)  discontinuous at x = . . . -9, -6, -3, 0, 3, 6, 9, . . .

Question 16

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial
function.
- f(x) =3x7−6x4+x+5f ( x )  = 3 x ^ { 7 } - 6 x ^ { 4 } + x + 5f(x) =3x7−6x4+x+5

Accepted Answer

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

Question 17

Determine whether the function is an even function, an odd function, or neither.
- f(x) =x3+x2−4f ( x )  = x ^ { 3 } + x ^ { 2 } - 4f(x) =x3+x2−4

Accepted Answer

A)  Odd
B)  Neither
C)  Even

Question 18

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s) of
discontinuity.
- f(x) =x2+8x+12f ( x )  = x ^ { 2 } + 8 x + 12f(x) =x2+8x+12

Accepted Answer

A)  discontinuous at x = 2 and x = 6
B)  discontinuous at x = -2 and x = -6
C)  continuous
D)     discontinuous at x=−23	ext { discontinuous at } x = - \frac { 2 } { 3 } discontinuous at x=−32​

Question 19

Determine which of the given graphs could be the graph of the given polynomial function.
- P(x) =4x5+5x3−16x2+8P ( x )  = 4 x ^ { 5 } + 5 x ^ { 3 } - 16 x ^ { 2 } + 8P(x) =4x5+5x3−16x2+8

Accepted Answer

A)   
B)   
C)   
D)

Question 20

Graph the polynomial function.
- f(x) =x4−5x3+5x2+5x−6f ( x )  = x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } + 5 x - 6f(x) =x4−5x3+5x2+5x−6

Accepted Answer

A)   
B)   
C)   
D)

Exam 10: Characteristics of Functions and Their Graphs

Find the x-intercepts of the function. - f(x) =(x+15) 2(x+9) 5f ( x ) = \left( x + \frac { 1 } { 5 } \right) ^ { 2 } ( x + 9 ) ^ { 5 }f(x) =(x+51​) 2(x+9) 5

Correct AnswerverifiedShow Answer

Find all the rational zeros of the function. - f(x) =x4+x2−2f ( x ) = x ^ { 4 } + x ^ { 2 } - 2f(x) =x4+x2−2

Correct AnswerverifiedShow Answer

Graph the polynomial function. - f(x) =x4−5x2+4f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4f(x) =x4−5x2+4

Correct AnswerverifiedShow Answer

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - f(x) =3x7−6x4+x+5f ( x ) = 3 x ^ { 7 } - 6 x ^ { 4 } + x + 5f(x) =3x7−6x4+x+5

Correct AnswerverifiedShow Answer

Find all real zeros (estimate the irrational zeros to the nearest hundredth) . - f(x) =x3+6x2+5x+30f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x + 30f(x) =x3+6x2+5x+30

Correct AnswerverifiedShow Answer

Graph the polynomial function. - f(x) =x4−5x3+5x2+5x−6f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } + 5 x - 6f(x) =x4−5x3+5x2+5x−6

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s) of discontinuity. - f(x) =⟦x3⟧f ( x ) = \llbracket \frac { x } { 3 } \rrbracketf(x) =[[3x​]]

Correct AnswerverifiedShow Answer

Find all the rational zeros of the function. - f(x) =2x3−9x2+7x+6f ( x ) = 2 x ^ { 3 } - 9 x ^ { 2 } + 7 x + 6f(x) =2x3−9x2+7x+6

Correct AnswerverifiedShow Answer

Graph the rational function. - f(x) =2x(x−2) (x+4) f ( x ) = \frac { 2 x } { ( x - 2 ) ( x + 4 ) }f(x) =(x−2) (x+4) 2x​

Correct AnswerverifiedShow Answer

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - g(x) =xx+5g ( x ) = \frac { x } { x + 5 }g(x) =x+5x​

Correct AnswerverifiedShow Answer

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s) of discontinuity. - f(x) =x2+8x+12f ( x ) = x ^ { 2 } + 8 x + 12f(x) =x2+8x+12

Correct AnswerverifiedShow Answer

Find the x-intercepts of the function. - f(x) =x3+x2−30xf ( x ) = x ^ { 3 } + x ^ { 2 } - 30 xf(x) =x3+x2−30x

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) =x3+3x2+8xf ( x ) = \frac { x ^ { 3 } + 3 } { x ^ { 2 } + 8 x }f(x) =x2+8xx3+3​

Correct AnswerverifiedShow Answer

Determine whether the function is an even function, an odd function, or neither. - f(x) =x3+x2−4f ( x ) = x ^ { 3 } + x ^ { 2 } - 4f(x) =x3+x2−4

Correct AnswerverifiedShow Answer

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - f(x) =x2−25f ( x ) = x ^ { 2 } - 25f(x) =x2−25

Correct AnswerverifiedShow Answer

Determine whether the function is an even function, an odd function, or neither. - g(x) =e3x+5g ( x ) = e ^ { 3 x } + 5g(x) =e3x+5

Correct AnswerverifiedShow Answer

Graph the greatest integer function. - f(x) =⟦13x⟧f ( x ) = \llbracket \frac { 1 } { 3 } x \rrbracketf(x) =[[31​x]]

Correct AnswerverifiedShow Answer

Determine which of the given graphs could be the graph of the given polynomial function. - P(x) =4x5+5x3−16x2+8P ( x ) = 4 x ^ { 5 } + 5 x ^ { 3 } - 16 x ^ { 2 } + 8P(x) =4x5+5x3−16x2+8

Correct AnswerverifiedShow Answer

Use the Intermediate Value Theorem to determine if a real zero of f(x) occurs in the given interval. If this cannot be determined, indicate so. - f(x) =2x4−7x3+4x2−x+4 in (2,3) f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 4 x ^ { 2 } - x + 4 \text { in } ( 2,3 ) f(x) =2x4−7x3+4x2−x+4 in (2,3)

Correct AnswerverifiedShow Answer

Find the x-intercepts of the function. - $f ( x ) = \left( x + \frac { 1 } { 5 } \right) ^ { 2 } ( x + 9 ) ^ { 5 }$

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

Correct Answer
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Graph the polynomial function. - $f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4$ $Graph the polynomial function. - f ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4 A) B) C) D)$

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. - $f ( x ) = 3 x ^ { 7 } - 6 x ^ { 4 } + x + 5$

Correct Answer
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Find all real zeros (estimate the irrational zeros to the nearest hundredth) . - $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } + 5 x + 30$

Correct Answer
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Graph the polynomial function. - $f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } + 5 x - 6$ $Graph the polynomial function. - f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } + 5 x - 6 A) B) C) D)$

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

Correct Answer
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Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s) of discontinuity. - $f ( x ) = \llbracket \frac { x } { 3 } \rrbracket$

Correct Answer
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Find all the rational zeros of the function. - $f ( x ) = 2 x ^ { 3 } - 9 x ^ { 2 } + 7 x + 6$

Correct Answer
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Graph the rational function. - $f ( x ) = \frac { 2 x } { ( x - 2 ) ( x + 4 ) }$ $Graph the rational function. - f ( x ) = \frac { 2 x } { ( x - 2 ) ( x + 4 ) } A) B) C) D)$

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. - $g ( x ) = \frac { x } { x + 5 }$

Correct Answer
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Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s) of discontinuity. - $f ( x ) = x ^ { 2 } + 8 x + 12$

Correct Answer
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Find the x-intercepts of the function. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 30 x$

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. - $f ( x ) = \frac { x ^ { 3 } + 3 } { x ^ { 2 } + 8 x }$

Correct Answer
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Determine whether the function is an even function, an odd function, or neither. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 4$

Correct Answer
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Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 2 } - 25$

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

Correct Answer
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Graph the greatest integer function. - $f ( x ) = \llbracket \frac { 1 } { 3 } x \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket \frac { 1 } { 3 } x \rrbracket A) B) C) D)$

Correct Answer
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Determine which of the given graphs could be the graph of the given polynomial function. - $P ( x ) = 4 x ^ { 5 } + 5 x ^ { 3 } - 16 x ^ { 2 } + 8$

Correct Answer
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Use the Intermediate Value Theorem to determine if a real zero of f(x) occurs in the given interval. If this cannot be determined, indicate so. - $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 4 x ^ { 2 } - x + 4 \text { in } ( 2,3 )$

Correct Answer
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