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. - $f ( x ) = \frac { 10 x ^ { 3 } - 17 x ^ { 2 } + 3 x - 1 } { 4 x ^ { 2 } - 1 }$

(Multiple Choice)

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Question 21

Solve the problem. -A paddle boat rental company rents paddle boats by the hour. They charge $7.00 per hour for the first 3 rental hours and $5.00 per hour for each additional hour. Write a piecewise function to represent the cost of renting a Paddle boat as a function of hours it is rented.

(Multiple Choice)

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Question 22

Determine the minimum degree of the polynomial function graphed. -

(Multiple Choice)

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Question 23

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x ^ { 2 } + 12 x + 35 } { x ^ { 2 } - 12 x + 35 }$

(Multiple Choice)

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Question 24

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 20 x$

(Multiple Choice)

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Question 25

Find the x-intercepts of the function. - $f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right)$

(Multiple Choice)

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Question 26

Graph the piecewise function. - $f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } x \leq - 2 \\- 2 x + 2 & \text { if } - 2 < x \leq 2 \\x + 1 & \text { if } x > 2\end{array} \right.$ $Graph the piecewise function. - f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } x \leq - 2 \\ - 2 x + 2 & \text { if } - 2 < x \leq 2 \\ x + 1 & \text { if } x > 2 \end{array} \right.$

(Multiple Choice)

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Question 27

List the possible rational zeros of the function. - $x ^ { 5 } - 5 x ^ { 2 } + 5 x + 7$

(Multiple Choice)

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Question 28

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 2 } - 16 x + 64$

(Multiple Choice)

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Question 29

Find all the zeros (real and complex)of the function. - $f ( x ) = 3 x ^ { 4 } - 23 x ^ { 3 } + 89 x ^ { 2 } - 167 x + 78$

(Multiple Choice)

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Question 30

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. - $f ( x ) = x ^ { 5 } + 2 x ^ { 4 } - 2 x ^ { 3 } + 2 x ^ { 2 } - 5 x - 3 \text { in } ( - 1,0 )$

(Multiple Choice)

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Question 31

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = 2 x ^ { 2 } - 26$

(Multiple Choice)

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Question 32

Graph the rational function. - $f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }$ $Graph the rational function. - f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }$

(Multiple Choice)

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Question 33

Graph the piecewise function. - $f ( x ) = \left\{ \begin{array} { l l } x + 5 & \text { if } x > 4 \\- ( x + 5 ) & \text { if } x \leq 4\end{array} \right.$ $Graph the piecewise function. - f ( x ) = \left\{ \begin{array} { l l } x + 5 & \text { if } x > 4 \\ - ( x + 5 ) & \text { if } x \leq 4 \end{array} \right.$

(Multiple Choice)

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Question 34

Determine the minimum degree of the polynomial function graphed. - $f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 )$ $Determine the minimum degree of the polynomial function graphed. - f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 )$

(Multiple Choice)

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Question 35

Find all the zeros (real and complex)of the function. - $f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64$

(Multiple Choice)

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Question 36

Determine whether the function is an even function, an odd function, or neither. - $f ( x ) = x ^ { 5 } - x ^ { 4 }$

(Multiple Choice)

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Question 37

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - $f ( x ) = 5 x ^ { 9 } - 4 x ^ { 8 } + x ^ { 7 } + 2.5 x + 15$

(Multiple Choice)

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Question 38

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

(Multiple Choice)

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Question 39

Graph the greatest integer function. - $f ( x ) = \llbracket x - 2 \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket x - 2 \rrbracket$

(Multiple Choice)

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Question 40

Showing 21 - 40 of 142

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. - $f ( x ) = \frac { 10 x ^ { 3 } - 17 x ^ { 2 } + 3 x - 1 } { 4 x ^ { 2 } - 1 }$

Solve the problem. -A paddle boat rental company rents paddle boats by the hour. They charge $7.00 per hour for the first 3 rental hours and $5.00 per hour for each additional hour. Write a piecewise function to represent the cost of renting a Paddle boat as a function of hours it is rented.

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. - $f ( x ) = \frac { x ^ { 2 } + 12 x + 35 } { x ^ { 2 } - 12 x + 35 }$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 20 x$

Find the x-intercepts of the function. - $f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right)$

List the possible rational zeros of the function. - $x ^ { 5 } - 5 x ^ { 2 } + 5 x + 7$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 2 } - 16 x + 64$

Find all the zeros (real and complex)of the function. - $f ( x ) = 3 x ^ { 4 } - 23 x ^ { 3 } + 89 x ^ { 2 } - 167 x + 78$

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. - $f ( x ) = x ^ { 5 } + 2 x ^ { 4 } - 2 x ^ { 3 } + 2 x ^ { 2 } - 5 x - 3 \text { in } ( - 1,0 )$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = 2 x ^ { 2 } - 26$

Graph the rational function. - $f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }$ $Graph the rational function. - f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }$

Determine the minimum degree of the polynomial function graphed. - $f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 )$ $Determine the minimum degree of the polynomial function graphed. - f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 )$

Find all the zeros (real and complex)of the function. - $f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64$

Determine whether the function is an even function, an odd function, or neither. - $f ( x ) = x ^ { 5 } - x ^ { 4 }$

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - $f ( x ) = 5 x ^ { 9 } - 4 x ^ { 8 } + x ^ { 7 } + 2.5 x + 15$

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

Graph the greatest integer function. - $f ( x ) = \llbracket x - 2 \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket x - 2 \rrbracket$

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

Solve the problem. -A paddle boat rental company rents paddle boats by the hour. They charge $7.00 per hour for the first 3 rental hours and $5.00 per hour for each additional hour. Write a piecewise function to represent the cost of renting a Paddle boat as a function of hours it is rented.

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+12x+35x2−12x+35f ( x ) = \frac { x ^ { 2 } + 12 x + 35 } { x ^ { 2 } - 12 x + 35 }f(x)=x2−12x+35x2+12x+35​

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - f(x)=x3+x2−20xf ( x ) = x ^ { 3 } + x ^ { 2 } - 20 xf(x)=x3+x2−20x

Find the x-intercepts of the function. - f(x)=x5(x2−25)(x2+16)f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right)f(x)=x5(x2−25)(x2+16)

List the possible rational zeros of the function. - x5−5x2+5x+7x ^ { 5 } - 5 x ^ { 2 } + 5 x + 7x5−5x2+5x+7

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - f(x)=x2−16x+64f ( x ) = x ^ { 2 } - 16 x + 64f(x)=x2−16x+64

Find all the zeros (real and complex)of the function. - f(x)=3x4−23x3+89x2−167x+78f ( x ) = 3 x ^ { 4 } - 23 x ^ { 3 } + 89 x ^ { 2 } - 167 x + 78f(x)=3x4−23x3+89x2−167x+78

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - f(x)=2x2−26f ( x ) = 2 x ^ { 2 } - 26f(x)=2x2−26

Graph the rational function. - f(x)=x3+2x2+4x+8x+2f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }f(x)=x+2x3+2x2+4x+8​

Graph the piecewise function. - f(x)={x+5 if x>4−(x+5) if x≤4f ( x ) = \left\{ \begin{array} { l l } x + 5 & \text { if } x > 4 \\- ( x + 5 ) & \text { if } x \leq 4\end{array} \right.f(x)={x+5−(x+5)​ if x>4 if x≤4​

Determine the minimum degree of the polynomial function graphed. - f(x)=x2(x−5)(x−1)f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 )f(x)=x2(x−5)(x−1)

Find all the zeros (real and complex)of the function. - f(x)=x4−12x2−64f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64f(x)=x4−12x2−64

Determine whether the function is an even function, an odd function, or neither. - f(x)=x5−x4f ( x ) = x ^ { 5 } - x ^ { 4 }f(x)=x5−x4

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - f(x)=5x9−4x8+x7+2.5x+15f ( x ) = 5 x ^ { 9 } - 4 x ^ { 8 } + x ^ { 7 } + 2.5 x + 15f(x)=5x9−4x8+x7+2.5x+15

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)=x4+4x3−4x2+5x+2 in (3,4)f ( x ) = x ^ { 4 } + 4 x ^ { 3 } - 4 x ^ { 2 } + 5 x + 2 \text { in } ( 3,4 )f(x)=x4+4x3−4x2+5x+2 in (3,4)

Graph the greatest integer function. - f(x)=⟦x−2⟧f ( x ) = \llbracket x - 2 \rrbracketf(x)=[[x−2]]

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

Find all points of discontinuity, and determine whether there is a hole or a vertical asymptote at each point. - $f ( x ) = \frac { x ^ { 2 } + 12 x + 35 } { x ^ { 2 } - 12 x + 35 }$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 20 x$

Find the x-intercepts of the function. - $f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right)$

List the possible rational zeros of the function. - $x ^ { 5 } - 5 x ^ { 2 } + 5 x + 7$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 2 } - 16 x + 64$

Find all the zeros (real and complex)of the function. - $f ( x ) = 3 x ^ { 4 } - 23 x ^ { 3 } + 89 x ^ { 2 } - 167 x + 78$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = 2 x ^ { 2 } - 26$

Graph the rational function. - $f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }$ $Graph the rational function. - f ( x ) = \frac { x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 } { x + 2 }$

Determine the minimum degree of the polynomial function graphed. - $f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 )$ $Determine the minimum degree of the polynomial function graphed. - f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 1 )$

Find all the zeros (real and complex)of the function. - $f ( x ) = x ^ { 4 } - 12 x ^ { 2 } - 64$

Determine whether the function is an even function, an odd function, or neither. - $f ( x ) = x ^ { 5 } - x ^ { 4 }$

Determine the maximum and minimum number of x-intercepts for the graph of the polynomial function. Do not graph the function. - $f ( x ) = 5 x ^ { 9 } - 4 x ^ { 8 } + x ^ { 7 } + 2.5 x + 15$

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

Graph the greatest integer function. - $f ( x ) = \llbracket x - 2 \rrbracket$ $Graph the greatest integer function. - f ( x ) = \llbracket x - 2 \rrbracket$