Exam 10: Characteristics of Functions and Their Graphs

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

(Multiple Choice)

4.9/5

(33)

Question 61

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

(Multiple Choice)

4.8/5

(32)

Question 62

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

(Multiple Choice)

4.9/5

(35)

Question 63

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

(Multiple Choice)

4.8/5

(38)

Question 64

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

(Multiple Choice)

4.9/5

(38)

Question 65

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

(Multiple Choice)

4.9/5

(40)

Question 66

Graph the greatest integer function. - $f ( x ) = \llbracket \frac { 1 } { 3 } x \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket \frac { 1 } { 3 } x \rrbracket$

(Multiple Choice)

4.8/5

(36)

Question 67

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

(Multiple Choice)

4.7/5

(35)

Question 68

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. - $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 4 x ^ { 2 } - x + 4 \text { in } ( 2,3 )$

(Multiple Choice)

4.8/5

(25)

Question 69

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

(Multiple Choice)

4.8/5

(41)

Question 70

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

(Multiple Choice)

4.9/5

(37)

Question 71

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

(Multiple Choice)

5.0/5

(20)

Question 72

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

(Multiple Choice)

5.0/5

(34)

Question 73

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

(Multiple Choice)

4.8/5

(34)

Question 74

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

(Multiple Choice)

4.8/5

(41)

Question 75

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

(Multiple Choice)

4.8/5

(27)

Question 76

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

(Multiple Choice)

4.9/5

(29)

Question 77

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

(Multiple Choice)

4.9/5

(32)

Question 78

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

(Multiple Choice)

4.8/5

(38)

Question 79

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

(Multiple Choice)

4.9/5

(46)

Question 80

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

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

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

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

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

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

Graph the greatest integer function. - $f ( x ) = \llbracket \frac { 1 } { 3 } x \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket \frac { 1 } { 3 } x \rrbracket$

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

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. - $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 4 x ^ { 2 } - x + 4 \text { in } ( 2,3 )$

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

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

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

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

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

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

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

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

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

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

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

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 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​

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

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

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

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

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

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

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

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)

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

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

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

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​]]

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

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

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

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

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

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​

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​

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

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

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

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

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

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

Graph the greatest integer function. - $f ( x ) = \llbracket \frac { 1 } { 3 } x \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket \frac { 1 } { 3 } x \rrbracket$

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

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. - $f ( x ) = 2 x ^ { 4 } - 7 x ^ { 3 } + 4 x ^ { 2 } - x + 4 \text { in } ( 2,3 )$

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

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

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

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

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

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

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

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

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

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

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