Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A) 2 
B) 1 
C) 0 
D) 3 
A) 2 
B) 1 
C) 0 
D) 3 C

Question 3

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

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 
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 D

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.
-$f ( x ) = \frac { 5 x ^ { 2 } + 20 x + 30 } { x - 4 }$

Accepted Answer

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

Question 5

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

Accepted Answer

A)  $x = - \frac { 1 } { 3 }$, multiplicity: 2
$x = 2$, multiplicity: 3 
B)  $x = \frac { 1 } { 3 }$, multiplicity: 2
$x = - 2$, multiplicity: 3 
C)  $x = - \frac { 1 } { 3 }$, multiplicity: 2
$x = 2$, multiplicity: 2 
D)  $x = \frac { 1 } { 3 }$, multiplicity: 2
$x = 2$, multiplicity: 3 
A)  $x = - \frac { 1 } { 3 }$, multiplicity: 2
$x = 2$, multiplicity: 3 
B)  $x = \frac { 1 } { 3 }$, multiplicity: 2
$x = - 2$, multiplicity: 3 
C)  $x = - \frac { 1 } { 3 }$, multiplicity: 2
$x = 2$, multiplicity: 2 
D)  $x = \frac { 1 } { 3 }$, multiplicity: 2
$x = 2$, multiplicity: 3

Question 6

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

Accepted Answer

A) Even 
B) Neither 
C) Odd 
A) Even 
B) Neither 
C) Odd

Question 7

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.
-$f ( x ) = \frac { 15 x } { 5 x ^ { 2 } + 1 }$

Accepted Answer

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

Question 8

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

Accepted Answer

A) 4 
B) 16 
C) 5 
D) 2 
A) 4 
B) 16 
C) 5 
D) 2

Question 9

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

Accepted Answer

A)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2 , \pm 3$ 
B)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2$ 
C)  $\pm \frac { 1 } { 2 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
D)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2$ 
A)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2 , \pm 3$ 
B)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2$ 
C)  $\pm \frac { 1 } { 2 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6$ 
D)  $\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm 1 , \pm 2$

Question 10

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

Accepted Answer

A) Even 
B) Neither 
C) Odd 
A) Even 
B) Neither 
C) Odd

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Determine the minimum degree of the polynomial function graphed.
-

Accepted Answer

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

Question 14

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)  $\text { discontinuous at } x = - \frac { 3 } { 4 }$ 
C)  $\text { discontinuous at } x = \frac { 3 } { 4 }$ 
D) continuous 
A) discontinuous at x = -3 
B)  $\text { discontinuous at } x = - \frac { 3 } { 4 }$ 
C)  $\text { discontinuous at } x = \frac { 3 } { 4 }$ 
D) continuous

Question 15

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

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 
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

Question 16

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.
-$f ( x ) = - 9 x ^ { 3 }$

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 
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

Question 17

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

Accepted Answer

A) 3 
B) 1 
C) 4 
D) 0 
A) 3 
B) 1 
C) 4 
D) 0

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

A) 0 
B) 1 
C) 3 
D) 2 
A) 0 
B) 1 
C) 3 
D) 2

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

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

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

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. - $f ( x ) = \frac { 5 x ^ { 2 } + 20 x + 30 } { x - 4 }$

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

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

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. - $f ( x ) = \frac { 15 x } { 5 x ^ { 2 } + 1 }$

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

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

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

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

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

Determine the minimum degree of the polynomial function graphed. -

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

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

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. - $f ( x ) = - 9 x ^ { 3 }$

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

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

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

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

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

Exam 10: Characteristics of Functions and Their Graphs

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)

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

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

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​

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

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

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​

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)

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

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

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

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)

Determine the minimum degree of the polynomial function graphed. -

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

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

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

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)

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​

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

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

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

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

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

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

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. - $f ( x ) = \frac { 5 x ^ { 2 } + 20 x + 30 } { x - 4 }$

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

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

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. - $f ( x ) = \frac { 15 x } { 5 x ^ { 2 } + 1 }$

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

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

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

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

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

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

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. - $f ( x ) = - 9 x ^ { 3 }$

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

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

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

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