Exam 3: Polynomial and Rational Functions

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -To locate the vertical asymptotes of a function, determine the real numbers x where the denominator is zero, but the numerator is .

(Short Answer)

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Question 181

Refer to the graph of the function and complete the statements. -The domain isـــــــــــ The range is ــــــــــــــ

(Multiple Choice)

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Question 182

Solve the problem. - $f ( x ) = - 9 x ^ { 2 } + 4 x + 6$

(Multiple Choice)

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Question 183

Write the function in vertex form and determine the x-intercept(s) - $h ( x ) = - 5 x ^ { 2 } + 11 x$

(Multiple Choice)

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Question 184

Solve the problem. -The period of a pendulum is the length of time required to complete one swing back and forth. The period varies directly as the square root of the length of the pendulum. If it takes $1.6 \mathrm { sec }$ for a $0.64 \mathrm {~m}$ pendulum to complete one period, what is the period of a $1.21 \mathrm {~m}$ pendulum?

(Multiple Choice)

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Question 185

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If k is a nonzero constant real number, then the statement y = kx implies that y varies as x.

(Short Answer)

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Question 186

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } - 6 x + 16 < 0$

(Multiple Choice)

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Question 187

Solve the problem. -A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminum that is 24 in. long and 8 in. wide. He makes A fold along the two long sides a distance of x inches from the edge. a. Write a function to represent the volume in terms of $x$ , b. What value of $x$ will maximize the volume of water that can be carried by the gutter?

(Multiple Choice)

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Question 188

Use the factor theorem to determine if the given binomial is a factor of f (x). - $f ( x ) = x ^ { 3 } + 343$ a. $x - 7$ b. $x + 7$

(Multiple Choice)

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Question 189

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

(Multiple Choice)

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Question 190

Solve the problem. -Find $m$ so that $x + 4$ is a factor of $5 x ^ { 3 } + 18 x ^ { 2 } + m x + 16$

(Multiple Choice)

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Question 191

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $4 ( x + 2 ) ( 8 x + 7 ) ^ { 3 } ( x + 2 ) ^ { 5 }$

(Multiple Choice)

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Question 192

Solve the inequality. Write the solution set in interval notation. - $7 y ^ { 2 } + 5 y \leq - 9 ( 7 y + 5 )$

(Multiple Choice)

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Question 193

Sketch the function. - $m ( x ) = - \frac { 1 } { 10 } ( x + 2 ) ( x - 2 ) ( x + 3 ) ^ { 3 }$

(Multiple Choice)

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Question 194

A polynomial f (x) and one of its zeros are given. Find all the zeros. - $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } + 30 x - 65 ; 3 - 2 i$ is a zero

(Multiple Choice)

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Question 195

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - $\text { The function given by } f ( x ) = - 3 x ^ { 5 } + \sqrt { 2 } x + \frac { 1 } { 2 } x \text { (is/is not) a polynomial function. }$

(Short Answer)

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Question 196

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The values of x in the domain of a polynomial function f for which $f ( x ) = 0$ are called the of the function.

(Short Answer)

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Question 197

Find all the zeros. - $f ( x ) = x ^ { 4 } - 13 x ^ { 2 } - 14$

(Multiple Choice)

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Question 198

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of $f ( x ) = - 6 x ^ { 2 }$ is (up/down) to the left and (up/down) to the right.

(Short Answer)

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Question 199

A function defined by $f ( x ) = a x ^ { 2 } + b x + c ( a \neq 0 )$ 0) is called a________ function.

(Short Answer)

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Question 200

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -To locate the vertical asymptotes of a function, determine the real numbers x where the denominator is zero, but the numerator is .

Refer to the graph of the function and complete the statements. -The domain isـــــــــــ The range is ــــــــــــــ

Solve the problem. - $f ( x ) = - 9 x ^ { 2 } + 4 x + 6$

Write the function in vertex form and determine the x-intercept(s) - $h ( x ) = - 5 x ^ { 2 } + 11 x$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If k is a nonzero constant real number, then the statement y = kx implies that y varies as x.

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } - 6 x + 16 < 0$

Use the factor theorem to determine if the given binomial is a factor of f (x). - $f ( x ) = x ^ { 3 } + 343$ a. $x - 7$ b. $x + 7$

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

Solve the problem. -Find $m$ so that $x + 4$ is a factor of $5 x ^ { 3 } + 18 x ^ { 2 } + m x + 16$

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $4 ( x + 2 ) ( 8 x + 7 ) ^ { 3 } ( x + 2 ) ^ { 5 }$

Solve the inequality. Write the solution set in interval notation. - $7 y ^ { 2 } + 5 y \leq - 9 ( 7 y + 5 )$

Sketch the function. - $m ( x ) = - \frac { 1 } { 10 } ( x + 2 ) ( x - 2 ) ( x + 3 ) ^ { 3 }$

A polynomial f (x) and one of its zeros are given. Find all the zeros. - $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } + 30 x - 65 ; 3 - 2 i$ is a zero

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - $\text { The function given by } f ( x ) = - 3 x ^ { 5 } + \sqrt { 2 } x + \frac { 1 } { 2 } x \text { (is/is not) a polynomial function. }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The values of x in the domain of a polynomial function f for which $f ( x ) = 0$ are called the of the function.

Find all the zeros. - $f ( x ) = x ^ { 4 } - 13 x ^ { 2 } - 14$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of $f ( x ) = - 6 x ^ { 2 }$ is (up/down) to the left and (up/down) to the right.

A function defined by $f ( x ) = a x ^ { 2 } + b x + c ( a \neq 0 )$ 0) is called a________ function.

Equations and Inequalities

Functions and Relations

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 3: Polynomial and Rational Functions

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -To locate the vertical asymptotes of a function, determine the real numbers x where the denominator is zero, but the numerator is .

Refer to the graph of the function and complete the statements. -The domain isـــــــــــ The range is ــــــــــــــ

Solve the problem. - f(x)=−9x2+4x+6f ( x ) = - 9 x ^ { 2 } + 4 x + 6f(x)=−9x2+4x+6

Write the function in vertex form and determine the x-intercept(s) - h(x)=−5x2+11xh ( x ) = - 5 x ^ { 2 } + 11 xh(x)=−5x2+11x

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If k is a nonzero constant real number, then the statement y = kx implies that y varies as x.

Solve the inequality. Write the solution set in interval notation. - −x2−6x+16<0- x ^ { 2 } - 6 x + 16 < 0−x2−6x+16<0

Use the factor theorem to determine if the given binomial is a factor of f (x). - f(x)=x3+343f ( x ) = x ^ { 3 } + 343f(x)=x3+343 a. x−7x - 7x−7 b. x+7x + 7x+7

Graph the function. - f(x)=4xx2−4x−5f ( x ) = \frac { 4 x } { x ^ { 2 } - 4 x - 5 }f(x)=x2−4x−54x​

Solve the problem. -Find mmm so that x+4x + 4x+4 is a factor of 5x3+18x2+mx+165 x ^ { 3 } + 18 x ^ { 2 } + m x + 165x3+18x2+mx+16

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - 4(x+2)(8x+7)3(x+2)54 ( x + 2 ) ( 8 x + 7 ) ^ { 3 } ( x + 2 ) ^ { 5 }4(x+2)(8x+7)3(x+2)5

Solve the inequality. Write the solution set in interval notation. - 7y2+5y≤−9(7y+5)7 y ^ { 2 } + 5 y \leq - 9 ( 7 y + 5 )7y2+5y≤−9(7y+5)

Sketch the function. - m(x)=−110(x+2)(x−2)(x+3)3m ( x ) = - \frac { 1 } { 10 } ( x + 2 ) ( x - 2 ) ( x + 3 ) ^ { 3 }m(x)=−101​(x+2)(x−2)(x+3)3

A polynomial f (x) and one of its zeros are given. Find all the zeros. - f(x)=x4−6x3+8x2+30x−65;3−2if ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } + 30 x - 65 ; 3 - 2 if(x)=x4−6x3+8x2+30x−65;3−2i is a zero

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The values of x in the domain of a polynomial function f for which f(x)=0f ( x ) = 0f(x)=0 are called the of the function.

Find all the zeros. - f(x)=x4−13x2−14f ( x ) = x ^ { 4 } - 13 x ^ { 2 } - 14f(x)=x4−13x2−14

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of f(x)=−6x2f ( x ) = - 6 x ^ { 2 }f(x)=−6x2 is (up/down) to the left and (up/down) to the right.

A function defined by f(x)=ax2+bx+c(a≠0)f ( x ) = a x ^ { 2 } + b x + c ( a \neq 0 )f(x)=ax2+bx+c(a=0) 0) is called a________ function.

Equations and Inequalities

Functions and Relations

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Solve the problem. - $f ( x ) = - 9 x ^ { 2 } + 4 x + 6$

Write the function in vertex form and determine the x-intercept(s) - $h ( x ) = - 5 x ^ { 2 } + 11 x$

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } - 6 x + 16 < 0$

Use the factor theorem to determine if the given binomial is a factor of f (x). - $f ( x ) = x ^ { 3 } + 343$ a. $x - 7$ b. $x + 7$

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

Solve the problem. -Find $m$ so that $x + 4$ is a factor of $5 x ^ { 3 } + 18 x ^ { 2 } + m x + 16$

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $4 ( x + 2 ) ( 8 x + 7 ) ^ { 3 } ( x + 2 ) ^ { 5 }$

Solve the inequality. Write the solution set in interval notation. - $7 y ^ { 2 } + 5 y \leq - 9 ( 7 y + 5 )$

Sketch the function. - $m ( x ) = - \frac { 1 } { 10 } ( x + 2 ) ( x - 2 ) ( x + 3 ) ^ { 3 }$

A polynomial f (x) and one of its zeros are given. Find all the zeros. - $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } + 30 x - 65 ; 3 - 2 i$ is a zero

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The values of x in the domain of a polynomial function f for which $f ( x ) = 0$ are called the of the function.

Find all the zeros. - $f ( x ) = x ^ { 4 } - 13 x ^ { 2 } - 14$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of $f ( x ) = - 6 x ^ { 2 }$ is (up/down) to the left and (up/down) to the right.

A function defined by $f ( x ) = a x ^ { 2 } + b x + c ( a \neq 0 )$ 0) is called a________ function.