Exam 4: Polynomial and Rational Functions

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. - $f ( x ) = 3 \left( x ^ { 2 } + 5 \right) ( x - 4 ) ^ { 2 }$

(Multiple Choice)

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Question 81

Solve the polynomial equation in the complex numbers. - $x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 = 0$

(Multiple Choice)

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Question 82

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 4$

(Multiple Choice)

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Question 83

Find the axis of symmetry of the quadratic function. - $f ( x ) = x ^ { 2 } - 4 x - 1$

(Multiple Choice)

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Question 84

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form. - $f ( x ) = x ^ { 4 } + 12 x ^ { 2 } - 64 ; c = 2$ is a zero

(Multiple Choice)

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Question 85

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f ( x ) = 4 x ^ { 2 } - 8 x + 8$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f ( x ) = 4 x ^ { 2 } - 8 x + 8$

(Multiple Choice)

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Question 86

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - $f ( x ) = x ^ { 8 } - 19$

(Multiple Choice)

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Question 87

Sketch the graph of the polynomial function. -

(Multiple Choice)

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Question 88

Find the range of the quadratic function in interval notation. - $f ( x ) = - 2 x ^ { 2 } - 4 x$

(Multiple Choice)

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Question 89

Solve the problem. -You have 192 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

(Multiple Choice)

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Question 90

Write the equation of the function in the form f(x)= ax2 + bx + c. -

(Multiple Choice)

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Question 91

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f(x)=-10 x^{2}-2 x-7$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=-10 x^{2}-2 x-7$

(Multiple Choice)

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Question 92

Graph the function using transformations. - $f(x)=\frac{1}{x^{2}}-4$ $Graph the function using transformations. - f(x)=\frac{1}{x^{2}}-4$

(Multiple Choice)

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Question 93

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x } { x + 9 }$

(Multiple Choice)

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Question 94

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 3 x ^ { 2 } + 19 x - 14 ; x - 7$

(Multiple Choice)

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Question 95

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x + 1 } { x ^ { 2 } - 1 }$

(Multiple Choice)

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Question 96

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } + 5 x + 2$

(Multiple Choice)

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Question 97

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = 2 x ^ { 2 } + 28 x + 90$

(Multiple Choice)

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Question 98

Graph the polynomial function. - $f(x)=-3 x(x-1)^{2}$ $Graph the polynomial function. - f(x)=-3 x(x-1)^{2}$

(Multiple Choice)

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Question 99

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 5$

(Multiple Choice)

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Question 100

Showing 81 - 100 of 255

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. - $f ( x ) = 3 \left( x ^ { 2 } + 5 \right) ( x - 4 ) ^ { 2 }$

Solve the polynomial equation in the complex numbers. - $x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 = 0$

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 4$

Find the axis of symmetry of the quadratic function. - $f ( x ) = x ^ { 2 } - 4 x - 1$

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form. - $f ( x ) = x ^ { 4 } + 12 x ^ { 2 } - 64 ; c = 2$ is a zero

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f ( x ) = 4 x ^ { 2 } - 8 x + 8$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f ( x ) = 4 x ^ { 2 } - 8 x + 8$

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - $f ( x ) = x ^ { 8 } - 19$

Sketch the graph of the polynomial function. -

Find the range of the quadratic function in interval notation. - $f ( x ) = - 2 x ^ { 2 } - 4 x$

Solve the problem. -You have 192 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

Write the equation of the function in the form f(x)= ax2 + bx + c. -

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f(x)=-10 x^{2}-2 x-7$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=-10 x^{2}-2 x-7$

Graph the function using transformations. - $f(x)=\frac{1}{x^{2}}-4$ $Graph the function using transformations. - f(x)=\frac{1}{x^{2}}-4$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x } { x + 9 }$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 3 x ^ { 2 } + 19 x - 14 ; x - 7$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x + 1 } { x ^ { 2 } - 1 }$

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } + 5 x + 2$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = 2 x ^ { 2 } + 28 x + 90$

Graph the polynomial function. - $f(x)=-3 x(x-1)^{2}$ $Graph the polynomial function. - f(x)=-3 x(x-1)^{2}$

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 5$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

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Exam 4: Polynomial and Rational Functions

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. - f(x)=3(x2+5)(x−4)2f ( x ) = 3 \left( x ^ { 2 } + 5 \right) ( x - 4 ) ^ { 2 }f(x)=3(x2+5)(x−4)2

Solve the polynomial equation in the complex numbers. - x3+2x2−6x+8=0x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 = 0x3+2x2−6x+8=0

Find the x-intercepts (if any) for the graph of the quadratic function. - f(x)=x2−4f ( x ) = x ^ { 2 } - 4f(x)=x2−4

Find the axis of symmetry of the quadratic function. - f(x)=x2−4x−1f ( x ) = x ^ { 2 } - 4 x - 1f(x)=x2−4x−1

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form. - f(x)=x4+12x2−64;c=2f ( x ) = x ^ { 4 } + 12 x ^ { 2 } - 64 ; c = 2f(x)=x4+12x2−64;c=2 is a zero

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=4x2−8x+8f ( x ) = 4 x ^ { 2 } - 8 x + 8f(x)=4x2−8x+8

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - f(x)=x8−19f ( x ) = x ^ { 8 } - 19f(x)=x8−19

Sketch the graph of the polynomial function. -

Find the range of the quadratic function in interval notation. - f(x)=−2x2−4xf ( x ) = - 2 x ^ { 2 } - 4 xf(x)=−2x2−4x

Solve the problem. -You have 192 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area.

Write the equation of the function in the form f(x)= ax2 + bx + c. -

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=−10x2−2x−7 f(x)=-10 x^{2}-2 x-7 f(x)=−10x2−2x−7

Graph the function using transformations. - f(x)=1x2−4f(x)=\frac{1}{x^{2}}-4f(x)=x21​−4

Find the vertical asymptotes, if any, of the graph of the rational function. - f(x)=xx+9f ( x ) = \frac { x } { x + 9 }f(x)=x+9x​

Use the Factor Theorem to determine whether x - c is a factor of f(x). - f(x)=x4+7x3+3x2+19x−14;x−7f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 3 x ^ { 2 } + 19 x - 14 ; x - 7f(x)=x4+7x3+3x2+19x−14;x−7

Find the vertical asymptotes, if any, of the graph of the rational function. - f(x)=x+1x2−1f ( x ) = \frac { x + 1 } { x ^ { 2 } - 1 }f(x)=x2−1x+1​

Rewrite the quadratic function in standard form by completing the square. - f(x)=x2+5x+2f ( x ) = x ^ { 2 } + 5 x + 2f(x)=x2+5x+2

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - f(x)=2x2+28x+90f ( x ) = 2 x ^ { 2 } + 28 x + 90f(x)=2x2+28x+90

Graph the polynomial function. - f(x)=−3x(x−1)2f(x)=-3 x(x-1)^{2}f(x)=−3x(x−1)2

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=x5−4x2+3x+5f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 5f(x)=x5−4x2+3x+5

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. - $f ( x ) = 3 \left( x ^ { 2 } + 5 \right) ( x - 4 ) ^ { 2 }$

Solve the polynomial equation in the complex numbers. - $x ^ { 3 } + 2 x ^ { 2 } - 6 x + 8 = 0$

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 4$

Find the axis of symmetry of the quadratic function. - $f ( x ) = x ^ { 2 } - 4 x - 1$

Find the remaining zeros of f(x)given that c is a zero. Then rewrite f(x)in completely factored form. - $f ( x ) = x ^ { 4 } + 12 x ^ { 2 } - 64 ; c = 2$ is a zero

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f ( x ) = 4 x ^ { 2 } - 8 x + 8$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f ( x ) = 4 x ^ { 2 } - 8 x + 8$

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - $f ( x ) = x ^ { 8 } - 19$

Find the range of the quadratic function in interval notation. - $f ( x ) = - 2 x ^ { 2 } - 4 x$

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f(x)=-10 x^{2}-2 x-7$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=-10 x^{2}-2 x-7$

Graph the function using transformations. - $f(x)=\frac{1}{x^{2}}-4$ $Graph the function using transformations. - f(x)=\frac{1}{x^{2}}-4$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x } { x + 9 }$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 3 x ^ { 2 } + 19 x - 14 ; x - 7$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x + 1 } { x ^ { 2 } - 1 }$

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } + 5 x + 2$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = 2 x ^ { 2 } + 28 x + 90$

Graph the polynomial function. - $f(x)=-3 x(x-1)^{2}$ $Graph the polynomial function. - f(x)=-3 x(x-1)^{2}$

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 4 x ^ { 2 } + 3 x + 5$