Exam 3: Polynomial and Rational Functions

Graph the function. - $f ( x ) = \frac { x ^ { 2 } + x - 12 } { x ^ { 2 } - x - 20 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } + x - 12 } { x ^ { 2 } - x - 20 }$

(Multiple Choice)

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Question 141

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: $- 3 , - 2,3$ ; degree 3

(Multiple Choice)

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Question 142

Use the graph to find the oblique asymptote, if any, of the function. -

(Multiple Choice)

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Question 143

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } - 7 } { 49 x - x ^ { 4 } }$

(Multiple Choice)

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Question 144

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { 8 } { x ^ { 2 } - 3 x - 23 }$

(Multiple Choice)

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Question 145

Use transformations of the graph o to graph the function. $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ - $f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2$ $Use transformations of the graph o to graph the function. y = x ^ { 4 } \text { or } y = x ^ { 5 } - f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2$

(Multiple Choice)

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Question 146

Use the graph to find the horizontal asymptote, if any, of the function. -

(Multiple Choice)

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Question 147

Use transformations of the graph o to graph the function. $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ - $f(x)=-\frac{1}{3} x^{4}$ $Use transformations of the graph o to graph the function. y = x ^ { 4 } \text { or } y = x ^ { 5 } - f(x)=-\frac{1}{3} x^{4}$

(Multiple Choice)

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Question 148

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x ^ { 3 } + 15 } { x ^ { 2 } - 5 }$

(Multiple Choice)

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Question 149

Use the given zero to find the remaining zeros of the function. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 \text {; zero: } 1 + i$

(Multiple Choice)

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Question 150

Solve the inequality. - $\frac { x - 2 } { x + 5 } < 0$

(Multiple Choice)

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Question 151

Write the word or phrase that best completes each statement or answers the question. The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. - $x ^ { 3 } - 8 x - 3 = 0 ; - 3 \leq r \leq - 2$

(Short Answer)

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Question 152

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -When two lenses are placed next to each other, their combined focal length (a measurement that can be negative or positive) is described by the equation $\mathrm { f } = \frac { \mathrm { f } _ { 1 } \mathrm { f } _ { 2 } } { \mathrm { f } _ { 1 } + \mathrm { f } _ { 2 } }$ If f1 = 0.001, what are the asymptotes of this function?

(Essay)

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Question 153

Give the equation of the horizontal asymptote, if any, of the function. - $h ( x ) = \frac { 4 x ^ { 3 } - 5 x - 9 } { 8 x + 3 }$

(Multiple Choice)

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Question 154

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 3 ; zeros: $- 3,3 - 5 i$

(Multiple Choice)

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Question 155

Graph the function using transformations. - $f ( x ) = \frac { - 2 } { x + 1 }$ $Graph the function using transformations. - f ( x ) = \frac { - 2 } { x + 1 }$

(Multiple Choice)

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Question 156

Use the graph to find the vertical asymptotes, if any, of the function. -

(Multiple Choice)

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Question 157

Solve the inequality. - $x ^ { 2 } - 8 x \geq 0$

(Multiple Choice)

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Question 158

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 4 ; zeros: $5 - 5 \mathrm { i }$ , $8 \mathrm { i }$

(Multiple Choice)

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Question 159

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = x + \frac { 25 } { x }$

(Multiple Choice)

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Question 160

Showing 141 - 160 of 354

Graph the function. - $f ( x ) = \frac { x ^ { 2 } + x - 12 } { x ^ { 2 } - x - 20 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } + x - 12 } { x ^ { 2 } - x - 20 }$

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: $- 3 , - 2,3$ ; degree 3

Use the graph to find the oblique asymptote, if any, of the function. -

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } - 7 } { 49 x - x ^ { 4 } }$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { 8 } { x ^ { 2 } - 3 x - 23 }$

Use transformations of the graph o to graph the function. $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ - $f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2$ $Use transformations of the graph o to graph the function. y = x ^ { 4 } \text { or } y = x ^ { 5 } - f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2$

Use the graph to find the horizontal asymptote, if any, of the function. -

Use transformations of the graph o to graph the function. $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ - $f(x)=-\frac{1}{3} x^{4}$ $Use transformations of the graph o to graph the function. y = x ^ { 4 } \text { or } y = x ^ { 5 } - f(x)=-\frac{1}{3} x^{4}$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x ^ { 3 } + 15 } { x ^ { 2 } - 5 }$

Use the given zero to find the remaining zeros of the function. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 \text {; zero: } 1 + i$

Solve the inequality. - $\frac { x - 2 } { x + 5 } < 0$

Write the word or phrase that best completes each statement or answers the question. The equation has a solution r in the interval indicated. Approximate this solution correct to two decimal places. - $x ^ { 3 } - 8 x - 3 = 0 ; - 3 \leq r \leq - 2$

Give the equation of the horizontal asymptote, if any, of the function. - $h ( x ) = \frac { 4 x ^ { 3 } - 5 x - 9 } { 8 x + 3 }$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 3 ; zeros: $- 3,3 - 5 i$

Graph the function using transformations. - $f ( x ) = \frac { - 2 } { x + 1 }$ $Graph the function using transformations. - f ( x ) = \frac { - 2 } { x + 1 }$

Use the graph to find the vertical asymptotes, if any, of the function. -

Solve the inequality. - $x ^ { 2 } - 8 x \geq 0$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 4 ; zeros: $5 - 5 \mathrm { i }$ , $8 \mathrm { i }$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = x + \frac { 25 } { x }$

Functions and Their Graphs

Linear and Quadratic Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 3: Polynomial and Rational Functions

Graph the function. - f(x)=x2+x−12x2−x−20f ( x ) = \frac { x ^ { 2 } + x - 12 } { x ^ { 2 } - x - 20 }f(x)=x2−x−20x2+x−12​

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: −3,−2,3- 3 , - 2,3−3,−2,3 ; degree 3

Use the graph to find the oblique asymptote, if any, of the function. -

Give the equation of the horizontal asymptote, if any, of the function. - f(x)=x2−749x−x4f ( x ) = \frac { x ^ { 2 } - 7 } { 49 x - x ^ { 4 } }f(x)=49x−x4x2−7​

Find the indicated intercept(s) of the graph of the function. - yyy -intercept of f(x)=8x2−3x−23f ( x ) = \frac { 8 } { x ^ { 2 } - 3 x - 23 }f(x)=x2−3x−238​

Use transformations of the graph o to graph the function. y=x4 or y=x5y = x ^ { 4 } \text { or } y = x ^ { 5 }y=x4 or y=x5 - f(x)=−2(x+3)5+2f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2f(x)=−2(x+3)5+2

Use the graph to find the horizontal asymptote, if any, of the function. -

Use transformations of the graph o to graph the function. y=x4 or y=x5y = x ^ { 4 } \text { or } y = x ^ { 5 }y=x4 or y=x5 - f(x)=−13x4f(x)=-\frac{1}{3} x^{4}f(x)=−31​x4

Find the indicated intercept(s) of the graph of the function. - yyy -intercept of f(x)=x3+15x2−5f ( x ) = \frac { x ^ { 3 } + 15 } { x ^ { 2 } - 5 }f(x)=x2−5x3+15​

Use the given zero to find the remaining zeros of the function. - f(x)=x3+2x2−6x+8; zero: 1+if ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 \text {; zero: } 1 + if(x)=x3+2x2−6x+8; zero: 1+i

Solve the inequality. - x−2x+5<0\frac { x - 2 } { x + 5 } < 0x+5x−2​<0

Give the equation of the horizontal asymptote, if any, of the function. - h(x)=4x3−5x−98x+3h ( x ) = \frac { 4 x ^ { 3 } - 5 x - 9 } { 8 x + 3 }h(x)=8x+34x3−5x−9​

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 3 ; zeros: −3,3−5i- 3,3 - 5 i−3,3−5i

Graph the function using transformations. - f(x)=−2x+1f ( x ) = \frac { - 2 } { x + 1 }f(x)=x+1−2​

Use the graph to find the vertical asymptotes, if any, of the function. -

Solve the inequality. - x2−8x≥0x ^ { 2 } - 8 x \geq 0x2−8x≥0

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 4 ; zeros: 5−5i5 - 5 \mathrm { i }5−5i , 8i8 \mathrm { i }8i

Find the indicated intercept(s) of the graph of the function. - yyy -intercept of f(x)=x+25xf ( x ) = x + \frac { 25 } { x }f(x)=x+x25​

Functions and Their Graphs

Linear and Quadratic Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Graph the function. - $f ( x ) = \frac { x ^ { 2 } + x - 12 } { x ^ { 2 } - x - 20 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } + x - 12 } { x ^ { 2 } - x - 20 }$

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. -Zeros: $- 3 , - 2,3$ ; degree 3

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { x ^ { 2 } - 7 } { 49 x - x ^ { 4 } }$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { 8 } { x ^ { 2 } - 3 x - 23 }$

Use transformations of the graph o to graph the function. $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ - $f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2$ $Use transformations of the graph o to graph the function. y = x ^ { 4 } \text { or } y = x ^ { 5 } - f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2$

Use transformations of the graph o to graph the function. $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ - $f(x)=-\frac{1}{3} x^{4}$ $Use transformations of the graph o to graph the function. y = x ^ { 4 } \text { or } y = x ^ { 5 } - f(x)=-\frac{1}{3} x^{4}$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = \frac { x ^ { 3 } + 15 } { x ^ { 2 } - 5 }$

Use the given zero to find the remaining zeros of the function. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 \text {; zero: } 1 + i$

Solve the inequality. - $\frac { x - 2 } { x + 5 } < 0$

Give the equation of the horizontal asymptote, if any, of the function. - $h ( x ) = \frac { 4 x ^ { 3 } - 5 x - 9 } { 8 x + 3 }$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 3 ; zeros: $- 3,3 - 5 i$

Graph the function using transformations. - $f ( x ) = \frac { - 2 } { x + 1 }$ $Graph the function using transformations. - f ( x ) = \frac { - 2 } { x + 1 }$

Solve the inequality. - $x ^ { 2 } - 8 x \geq 0$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 4 ; zeros: $5 - 5 \mathrm { i }$ , $8 \mathrm { i }$

Find the indicated intercept(s) of the graph of the function. - $y$ -intercept of $f ( x ) = x + \frac { 25 } { x }$