Question 1

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

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 10 } , \pm 5 , \pm 2 , \pm 10$ 
B)  $\pm 1 , \pm 5 , \pm 2$ 
C)  $\pm 1 , \pm 5 , \pm 2 , \pm 10$ 
D)  $\pm 1 , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 10 }$ 
A)  $\pm 1 , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 10 } , \pm 5 , \pm 2 , \pm 10$ 
B)  $\pm 1 , \pm 5 , \pm 2$ 
C)  $\pm 1 , \pm 5 , \pm 2 , \pm 10$ 
D)  $\pm 1 , \pm \frac { 1 } { 5 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 10 }$

Question 2

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

Accepted Answer

A)  $\text { Horizontal asymptote: } \mathrm { y } = - \frac { 1 } { 2 }$ 
B)  $\text { Oblique asymptote: } y = - \frac { 1 } { 2 } x - 5$ 
C) Neither 
A)  $\text { Horizontal asymptote: } \mathrm { y } = - \frac { 1 } { 2 }$ 
B)  $\text { Oblique asymptote: } y = - \frac { 1 } { 2 } x - 5$ 
C) Neither

Question 3

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.
-$f ( x ) = x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } - 9 x - 8 \text { in } [ - 1,4 ]$

Accepted Answer

A) Cannot determine 
B) Yes 
A) Cannot determine 
B) Yes

Question 4

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

Accepted Answer

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

Question 5

Classify the function as continuous or discontinuous.
-

Accepted Answer

A) continuous 
B) discontinuous 
A) continuous 
B) discontinuous

Question 6

Graph the greatest integer function.
-$f ( x ) = \llbracket \frac { x + 4 } { 3 } \rrbracket$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

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

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) 
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 8

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

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

Accepted Answer

A) continuous 
B) discontinuous at x = 6 
C)  $\text { discontinuous at } x = \frac { 6 } { 7 }$ 
D) discontinuous at x = -6 
A) continuous 
B) discontinuous at x = 6 
C)  $\text { discontinuous at } x = \frac { 6 } { 7 }$ 
D) discontinuous at x = -6

Question 10

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

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 
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 11

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

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 
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 12

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

Accepted Answer

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

Question 13

Determine the minimum degree of the polynomial function graphed.
-

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

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

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 
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 16

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Classify the function as continuous or discontinuous.
-

Accepted Answer

A) discontinuous 
B) continuous 
A) discontinuous 
B) continuous

Question 20

Classify the function as continuous or discontinuous.
-

Accepted Answer

A) discontinuous 
B) continuous 
A) discontinuous 
B) continuous

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

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

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. - $f ( x ) = x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } - 9 x - 8 \text { in } [ - 1,4 ]$

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

Classify the function as continuous or discontinuous. -

Graph the greatest integer function. - $f ( x ) = \llbracket \frac { x + 4 } { 3 } \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket \frac { x + 4 } { 3 } \rrbracket$

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

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

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

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

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

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

Determine the minimum degree of the polynomial function graphed. -

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

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

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

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

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

Classify the function as continuous or discontinuous. -

Classify the function as continuous or discontinuous. -

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and Probability

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Exam 10: Characteristics of Functions and Their Graphs

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

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​

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 \text { in } [ - 1,4 ]f(x)=x4−3x3+5x2−9x−8 in [−1,4]

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

Classify the function as continuous or discontinuous. -

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

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

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

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

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

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

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)

Determine the minimum degree of the polynomial function graphed. -

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​

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

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)

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

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​

Classify the function as continuous or discontinuous. -

Classify the function as continuous or discontinuous. -

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and Probability

Filters

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

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

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. - $f ( x ) = x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } - 9 x - 8 \text { in } [ - 1,4 ]$

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

Graph the greatest integer function. - $f ( x ) = \llbracket \frac { x + 4 } { 3 } \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket \frac { x + 4 } { 3 } \rrbracket$

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

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

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

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

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

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

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

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

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

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

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