Exam 3: Polynomial and Rational Functions

Solve the problem. -Determine if the lower bound theorem identifies -4 as a lower bound for the real zeros of f (x). $f ( x ) = 3 x ^ { 3 } + 2 x ^ { 2 } - 9 x + 4$

(Multiple Choice)

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Question 141

Solve the inequality. Write the solution set in interval notation. - $\frac { x ^ { 2 } } { x ^ { 2 } + 25 } \geq 0$

(Multiple Choice)

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Question 142

Choose the one alternative that best completes the statement or answers the question. Write the domain in interval notation. - $f ( x ) = \frac { 7 x - 1 } { 4 x ^ { 2 } - 27 x - 81 }$

(Multiple Choice)

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Question 143

Solve the inequality. Write the solution set in interval notation. - $( 7 x - 9 ) ( 5 x - 9 ) < 0$

(Multiple Choice)

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Question 144

A polynomial f (x) and one of its zeros are given. Factor f (x) as a product of linear factors. - $f ( x ) = 4 x ^ { 3 } - 23 x ^ { 2 } + 46 x + 13 ; \quad 3 + 2 i$ is a zero

(Multiple Choice)

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Question 145

Given $f ( x ) = a ( x - h ) ^ { 2 } + k ( a \neq 0 )$ he vertex of the parabola is the point ________.

(Short Answer)

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Question 146

Solve the problem. - $f ( x ) = x ^ { 4 } - 4 x ^ { 2 } - 221$ a. Factor the polynomial over the set of real numbers. b. Factor the polynomial over the set of complex numbers.

(Multiple Choice)

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Question 147

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - The graph of the function defined by $f ( x ) = | x |$ | is smooth.

(True/False)

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Question 148

Graph the function. - $g ( x ) = - \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } + 2$

(Multiple Choice)

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Question 149

Graph the function and determine the minimum or maximum value of the function. - $m ( x ) = - \frac { 1 } { 4 } ( x + 1 ) ^ { 2 }$

(Multiple Choice)

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Question 150

Solve the inequality. Write the solution set in interval notation. - $\frac { 7 x } { x + 2 } \geq 7$

(Multiple Choice)

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Question 151

Graph the function by using a transformation of the graph of $y = \frac { 1 } { x } .$ - $f ( x ) = \frac { 1 } { x + 2 }$

(Multiple Choice)

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Question 152

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the maximum number of turning points of the graph of $f ( x ) = - 3 x ^ { 6 } - 4 x ^ { 5 } - 5 x ^ { 4 } + 2 x ^ { 2 } + 6$

(Short Answer)

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Question 153

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Suppose that f is a polynomial function and that a < b. If f(a) and f(b) have opposite signs, then what conclusion can be drawn from the intermediate value theorem?

(Short Answer)

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Question 154

Sketch the function. - $f ( x ) = - x ^ { 4 } + 15 x ^ { 2 } - 44$

(Multiple Choice)

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Question 155

Find all the zeros. - $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 57 x - 82$

(Multiple Choice)

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Question 156

Solve the inequality. Write the solution set in interval notation. - $\frac { x + 6 } { x - 1 } > 0$

(Multiple Choice)

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Question 157

Find the constant of variation k. -p is inversely proportional to q. When q is 8, p is 3.

(Multiple Choice)

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Question 158

Find the zeros of the function and state the multiplicities. - $f ( x ) = [ x - ( 4 - \sqrt { 7 } ) ] [ x - ( 4 + \sqrt { 7 } ) ]$

(Multiple Choice)

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Question 159

Sketch the function. - $g ( x ) = \frac { 1 } { 6 } ( x - 5 ) ( x + 4 ) ( x + 1 )$

(Multiple Choice)

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Question 160

Solve the problem. -Determine if the lower bound theorem identifies -4 as a lower bound for the real zeros of f (x). $f ( x ) = 3 x ^ { 3 } + 2 x ^ { 2 } - 9 x + 4$

Solve the inequality. Write the solution set in interval notation. - $\frac { x ^ { 2 } } { x ^ { 2 } + 25 } \geq 0$

Choose the one alternative that best completes the statement or answers the question. Write the domain in interval notation. - $f ( x ) = \frac { 7 x - 1 } { 4 x ^ { 2 } - 27 x - 81 }$

Solve the inequality. Write the solution set in interval notation. - $( 7 x - 9 ) ( 5 x - 9 ) < 0$

A polynomial f (x) and one of its zeros are given. Factor f (x) as a product of linear factors. - $f ( x ) = 4 x ^ { 3 } - 23 x ^ { 2 } + 46 x + 13 ; \quad 3 + 2 i$ is a zero

Given $f ( x ) = a ( x - h ) ^ { 2 } + k ( a \neq 0 )$ he vertex of the parabola is the point ________.

Solve the problem. - $f ( x ) = x ^ { 4 } - 4 x ^ { 2 } - 221$ a. Factor the polynomial over the set of real numbers. b. Factor the polynomial over the set of complex numbers.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - The graph of the function defined by $f ( x ) = | x |$ | is smooth.

Graph the function. - $g ( x ) = - \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } + 2$

Graph the function and determine the minimum or maximum value of the function. - $m ( x ) = - \frac { 1 } { 4 } ( x + 1 ) ^ { 2 }$

Solve the inequality. Write the solution set in interval notation. - $\frac { 7 x } { x + 2 } \geq 7$

Graph the function by using a transformation of the graph of $y = \frac { 1 } { x } .$ - $f ( x ) = \frac { 1 } { x + 2 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the maximum number of turning points of the graph of $f ( x ) = - 3 x ^ { 6 } - 4 x ^ { 5 } - 5 x ^ { 4 } + 2 x ^ { 2 } + 6$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Suppose that f is a polynomial function and that a < b. If f(a) and f(b) have opposite signs, then what conclusion can be drawn from the intermediate value theorem?

Sketch the function. - $f ( x ) = - x ^ { 4 } + 15 x ^ { 2 } - 44$

Find all the zeros. - $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 57 x - 82$

Solve the inequality. Write the solution set in interval notation. - $\frac { x + 6 } { x - 1 } > 0$

Find the constant of variation k. -p is inversely proportional to q. When q is 8, p is 3.

Find the zeros of the function and state the multiplicities. - $f ( x ) = [ x - ( 4 - \sqrt { 7 } ) ] [ x - ( 4 + \sqrt { 7 } ) ]$

Sketch the function. - $g ( x ) = \frac { 1 } { 6 } ( x - 5 ) ( x + 4 ) ( x + 1 )$

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Exam 3: Polynomial and Rational Functions

Solve the problem. -Determine if the lower bound theorem identifies -4 as a lower bound for the real zeros of f (x). f(x)=3x3+2x2−9x+4f ( x ) = 3 x ^ { 3 } + 2 x ^ { 2 } - 9 x + 4f(x)=3x3+2x2−9x+4

Solve the inequality. Write the solution set in interval notation. - x2x2+25≥0\frac { x ^ { 2 } } { x ^ { 2 } + 25 } \geq 0x2+25x2​≥0

Choose the one alternative that best completes the statement or answers the question. Write the domain in interval notation. - f(x)=7x−14x2−27x−81f ( x ) = \frac { 7 x - 1 } { 4 x ^ { 2 } - 27 x - 81 }f(x)=4x2−27x−817x−1​

Solve the inequality. Write the solution set in interval notation. - (7x−9)(5x−9)<0( 7 x - 9 ) ( 5 x - 9 ) < 0(7x−9)(5x−9)<0

A polynomial f (x) and one of its zeros are given. Factor f (x) as a product of linear factors. - f(x)=4x3−23x2+46x+13;3+2if ( x ) = 4 x ^ { 3 } - 23 x ^ { 2 } + 46 x + 13 ; \quad 3 + 2 if(x)=4x3−23x2+46x+13;3+2i is a zero

Given f(x)=a(x−h)2+k(a≠0)f ( x ) = a ( x - h ) ^ { 2 } + k ( a \neq 0 )f(x)=a(x−h)2+k(a=0) he vertex of the parabola is the point ________.

Solve the problem. - f(x)=x4−4x2−221f ( x ) = x ^ { 4 } - 4 x ^ { 2 } - 221f(x)=x4−4x2−221 a. Factor the polynomial over the set of real numbers. b. Factor the polynomial over the set of complex numbers.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - The graph of the function defined by f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ | is smooth.

Graph the function. - g(x)=−12(x−1)2+2g ( x ) = - \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } + 2g(x)=−21​(x−1)2+2

Graph the function and determine the minimum or maximum value of the function. - m(x)=−14(x+1)2m ( x ) = - \frac { 1 } { 4 } ( x + 1 ) ^ { 2 }m(x)=−41​(x+1)2

Solve the inequality. Write the solution set in interval notation. - 7xx+2≥7\frac { 7 x } { x + 2 } \geq 7x+27x​≥7

Graph the function by using a transformation of the graph of y=1x.y = \frac { 1 } { x } .y=x1​. - f(x)=1x+2f ( x ) = \frac { 1 } { x + 2 }f(x)=x+21​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Suppose that f is a polynomial function and that a < b. If f(a) and f(b) have opposite signs, then what conclusion can be drawn from the intermediate value theorem?

Sketch the function. - f(x)=−x4+15x2−44f ( x ) = - x ^ { 4 } + 15 x ^ { 2 } - 44f(x)=−x4+15x2−44

Find all the zeros. - f(x)=x3−10x2+57x−82f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 57 x - 82f(x)=x3−10x2+57x−82

Solve the inequality. Write the solution set in interval notation. - x+6x−1>0\frac { x + 6 } { x - 1 } > 0x−1x+6​>0

Find the constant of variation k. -p is inversely proportional to q. When q is 8, p is 3.

Find the zeros of the function and state the multiplicities. - f(x)=[x−(4−7)][x−(4+7)]f ( x ) = [ x - ( 4 - \sqrt { 7 } ) ] [ x - ( 4 + \sqrt { 7 } ) ]f(x)=[x−(4−7​)][x−(4+7​)]

Sketch the function. - g(x)=16(x−5)(x+4)(x+1)g ( x ) = \frac { 1 } { 6 } ( x - 5 ) ( x + 4 ) ( x + 1 )g(x)=61​(x−5)(x+4)(x+1)

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. -Determine if the lower bound theorem identifies -4 as a lower bound for the real zeros of f (x). $f ( x ) = 3 x ^ { 3 } + 2 x ^ { 2 } - 9 x + 4$

Solve the inequality. Write the solution set in interval notation. - $\frac { x ^ { 2 } } { x ^ { 2 } + 25 } \geq 0$

Choose the one alternative that best completes the statement or answers the question. Write the domain in interval notation. - $f ( x ) = \frac { 7 x - 1 } { 4 x ^ { 2 } - 27 x - 81 }$

Solve the inequality. Write the solution set in interval notation. - $( 7 x - 9 ) ( 5 x - 9 ) < 0$

A polynomial f (x) and one of its zeros are given. Factor f (x) as a product of linear factors. - $f ( x ) = 4 x ^ { 3 } - 23 x ^ { 2 } + 46 x + 13 ; \quad 3 + 2 i$ is a zero

Given $f ( x ) = a ( x - h ) ^ { 2 } + k ( a \neq 0 )$ he vertex of the parabola is the point ________.

Solve the problem. - $f ( x ) = x ^ { 4 } - 4 x ^ { 2 } - 221$ a. Factor the polynomial over the set of real numbers. b. Factor the polynomial over the set of complex numbers.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - The graph of the function defined by $f ( x ) = | x |$ | is smooth.

Graph the function. - $g ( x ) = - \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } + 2$

Graph the function and determine the minimum or maximum value of the function. - $m ( x ) = - \frac { 1 } { 4 } ( x + 1 ) ^ { 2 }$

Solve the inequality. Write the solution set in interval notation. - $\frac { 7 x } { x + 2 } \geq 7$

Graph the function by using a transformation of the graph of $y = \frac { 1 } { x } .$ - $f ( x ) = \frac { 1 } { x + 2 }$

Sketch the function. - $f ( x ) = - x ^ { 4 } + 15 x ^ { 2 } - 44$

Find all the zeros. - $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 57 x - 82$

Solve the inequality. Write the solution set in interval notation. - $\frac { x + 6 } { x - 1 } > 0$

Find the zeros of the function and state the multiplicities. - $f ( x ) = [ x - ( 4 - \sqrt { 7 } ) ] [ x - ( 4 + \sqrt { 7 } ) ]$

Sketch the function. - $g ( x ) = \frac { 1 } { 6 } ( x - 5 ) ( x + 4 ) ( x + 1 )$