Exam 4: Polynomial and Rational Functions

Graph the polynomial function. - $f ( x ) = - 2 x ^ { 3 } ( x + 1 ) ^ { 2 } ( x + 4 )$ $Graph the polynomial function. - f ( x ) = - 2 x ^ { 3 } ( x + 1 ) ^ { 2 } ( x + 4 )$

(Multiple Choice)

4.7/5

(38)

Question 101

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { 4 x ^ { 2 } + 8 } { 4 x ^ { 2 } - 8 }$

(Multiple Choice)

4.8/5

(36)

Question 102

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

(Multiple Choice)

4.9/5

(37)

Question 103

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } + 3 x + 1$

(Multiple Choice)

4.8/5

(36)

Question 104

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 1 ) ( x - 8 ) ( x - 1 ) ^ { 2 }$

(Multiple Choice)

4.9/5

(45)

Question 105

For the following rational function, identify the coordinates of all removable discontinuities and sketch the graph. Identify all intercepts and find the equations of all asymptotes. - $f ( x ) = \frac { 3 x ^ { 2 } - 4 x - 4 } { x - 2 }$ $For the following rational function, identify the coordinates of all removable discontinuities and sketch the graph. Identify all intercepts and find the equations of all asymptotes. - f ( x ) = \frac { 3 x ^ { 2 } - 4 x - 4 } { x - 2 }$

(Multiple Choice)

4.9/5

(26)

Question 106

Graph the polynomial function. - $f ( x ) = 6 x ^ { 3 } - 5 x - x ^ { 5 }$ $Graph the polynomial function. - f ( x ) = 6 x ^ { 3 } - 5 x - x ^ { 5 }$

(Multiple Choice)

4.8/5

(33)

Question 107

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

(Multiple Choice)

4.9/5

(46)

Question 108

Graph the function. - $f(x)=\frac{x^{2}+4 x+3}{(x-1)^{2}}$ $Graph the function. - f(x)=\frac{x^{2}+4 x+3}{(x-1)^{2}}$

(Multiple Choice)

4.7/5

(31)

Question 109

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - $f ( x ) = - 4 x ^ { 7 } - 9 x ^ { 6 } - 4.5 x ^ { 5 } + 3 x ^ { 4 } + x + 18$

(Multiple Choice)

4.9/5

(33)

Question 110

Solve the polynomial equation in the complex numbers. - $3 x ^ { 3 } - x ^ { 2 } - 21 x + 7 = 0$

(Multiple Choice)

4.7/5

(35)

Question 111

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

(Multiple Choice)

4.8/5

(37)

Question 112

Find the range of the quadratic function in interval notation. - $f ( x ) = - x ^ { 2 } + 14 x + 2$

(Multiple Choice)

4.8/5

(40)

Question 113

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = x ^ { 2 } + 4 x - 3$

(Multiple Choice)

4.8/5

(37)

Question 114

Graph the polynomial function. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$ $Graph the polynomial function. - f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

(Multiple Choice)

4.9/5

(33)

Question 115

Use the intermediate value theorem to approximate the one real zero on the given interval. Round your answer to two decimal places. - $f ( x ) = x ^ { 3 } - 8 x - 3 ; [ - 3 , - 2 ]$

(Multiple Choice)

4.8/5

(26)

Question 116

Find the axis of symmetry of the quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } - 6$

(Multiple Choice)

4.9/5

(40)

Question 117

Solve the polynomial equation in the complex numbers. - $3 x ^ { 4 } + 20 x ^ { 3 } + 75 x ^ { 2 } + 120 x + 52 = 0$

(Multiple Choice)

4.7/5

(34)

Question 118

Solve the polynomial equation in the complex numbers. - $3 x ^ { 4 } - 22 x ^ { 3 } + 64 x ^ { 2 } - 58 x + 13 = 0$

(Multiple Choice)

4.7/5

(27)

Question 119

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 2 } - 2 x + 6$

(Multiple Choice)

4.9/5

(27)

Question 120

Showing 101 - 120 of 255

Graph the polynomial function. - $f ( x ) = - 2 x ^ { 3 } ( x + 1 ) ^ { 2 } ( x + 4 )$ $Graph the polynomial function. - f ( x ) = - 2 x ^ { 3 } ( x + 1 ) ^ { 2 } ( x + 4 )$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { 4 x ^ { 2 } + 8 } { 4 x ^ { 2 } - 8 }$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } + 3 x + 1$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 1 ) ( x - 8 ) ( x - 1 ) ^ { 2 }$

Graph the polynomial function. - $f ( x ) = 6 x ^ { 3 } - 5 x - x ^ { 5 }$ $Graph the polynomial function. - f ( x ) = 6 x ^ { 3 } - 5 x - x ^ { 5 }$

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

Graph the function. - $f(x)=\frac{x^{2}+4 x+3}{(x-1)^{2}}$ $Graph the function. - f(x)=\frac{x^{2}+4 x+3}{(x-1)^{2}}$

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - $f ( x ) = - 4 x ^ { 7 } - 9 x ^ { 6 } - 4.5 x ^ { 5 } + 3 x ^ { 4 } + x + 18$

Solve the polynomial equation in the complex numbers. - $3 x ^ { 3 } - x ^ { 2 } - 21 x + 7 = 0$

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

Find the range of the quadratic function in interval notation. - $f ( x ) = - x ^ { 2 } + 14 x + 2$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = x ^ { 2 } + 4 x - 3$

Graph the polynomial function. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$ $Graph the polynomial function. - f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Use the intermediate value theorem to approximate the one real zero on the given interval. Round your answer to two decimal places. - $f ( x ) = x ^ { 3 } - 8 x - 3 ; [ - 3 , - 2 ]$

Find the axis of symmetry of the quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } - 6$

Solve the polynomial equation in the complex numbers. - $3 x ^ { 4 } + 20 x ^ { 3 } + 75 x ^ { 2 } + 120 x + 52 = 0$

Solve the polynomial equation in the complex numbers. - $3 x ^ { 4 } - 22 x ^ { 3 } + 64 x ^ { 2 } - 58 x + 13 = 0$

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 2 } - 2 x + 6$

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

Exam 4: Polynomial and Rational Functions

Graph the polynomial function. - f(x)=−2x3(x+1)2(x+4)f ( x ) = - 2 x ^ { 3 } ( x + 1 ) ^ { 2 } ( x + 4 )f(x)=−2x3(x+1)2(x+4)

Find the vertical asymptotes, if any, of the graph of the rational function. - f(x)=4x2+84x2−8f ( x ) = \frac { 4 x ^ { 2 } + 8 } { 4 x ^ { 2 } - 8 }f(x)=4x2−84x2+8​

Use the graph of a power function and transformations to sketch the graph of the polynomial function. -

Rewrite the quadratic function in standard form by completing the square. - f(x)=x2+3x+1f ( x ) = x ^ { 2 } + 3 x + 1f(x)=x2+3x+1

Find the x- and y-intercepts of f. - f(x)=(x+1)(x−8)(x−1)2f ( x ) = ( x + 1 ) ( x - 8 ) ( x - 1 ) ^ { 2 }f(x)=(x+1)(x−8)(x−1)2

For the following rational function, identify the coordinates of all removable discontinuities and sketch the graph. Identify all intercepts and find the equations of all asymptotes. - f(x)=3x2−4x−4x−2f ( x ) = \frac { 3 x ^ { 2 } - 4 x - 4 } { x - 2 }f(x)=x−23x2−4x−4​

Graph the polynomial function. - f(x)=6x3−5x−x5f ( x ) = 6 x ^ { 3 } - 5 x - x ^ { 5 }f(x)=6x3−5x−x5

Graph the polynomial function. - f(x)=−x2(x+1)(x+3)f ( x ) = - x ^ { 2 } ( x + 1 ) ( x + 3 )f(x)=−x2(x+1)(x+3)

Graph the function. - f(x)=x2+4x+3(x−1)2f(x)=\frac{x^{2}+4 x+3}{(x-1)^{2}}f(x)=(x−1)2x2+4x+3​

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - f(x)=−4x7−9x6−4.5x5+3x4+x+18f ( x ) = - 4 x ^ { 7 } - 9 x ^ { 6 } - 4.5 x ^ { 5 } + 3 x ^ { 4 } + x + 18f(x)=−4x7−9x6−4.5x5+3x4+x+18

Solve the polynomial equation in the complex numbers. - 3x3−x2−21x+7=03 x ^ { 3 } - x ^ { 2 } - 21 x + 7 = 03x3−x2−21x+7=0

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

Find the range of the quadratic function in interval notation. - f(x)=−x2+14x+2f ( x ) = - x ^ { 2 } + 14 x + 2f(x)=−x2+14x+2

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - f(x)=x2+4x−3f ( x ) = x ^ { 2 } + 4 x - 3f(x)=x2+4x−3

Graph the polynomial function. - f(x)=x3+8x2−x−8f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8f(x)=x3+8x2−x−8

Use the intermediate value theorem to approximate the one real zero on the given interval. Round your answer to two decimal places. - f(x)=x3−8x−3;[−3,−2]f ( x ) = x ^ { 3 } - 8 x - 3 ; [ - 3 , - 2 ]f(x)=x3−8x−3;[−3,−2]

Find the axis of symmetry of the quadratic function. - f(x)=(x+4)2−6f ( x ) = ( x + 4 ) ^ { 2 } - 6f(x)=(x+4)2−6

Solve the polynomial equation in the complex numbers. - 3x4+20x3+75x2+120x+52=03 x ^ { 4 } + 20 x ^ { 3 } + 75 x ^ { 2 } + 120 x + 52 = 03x4+20x3+75x2+120x+52=0

Solve the polynomial equation in the complex numbers. - 3x4−22x3+64x2−58x+13=03 x ^ { 4 } - 22 x ^ { 3 } + 64 x ^ { 2 } - 58 x + 13 = 03x4−22x3+64x2−58x+13=0

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=−4x4+3x2−2x+6f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 2 } - 2 x + 6f(x)=−4x4+3x2−2x+6

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

Graph the polynomial function. - $f ( x ) = - 2 x ^ { 3 } ( x + 1 ) ^ { 2 } ( x + 4 )$ $Graph the polynomial function. - f ( x ) = - 2 x ^ { 3 } ( x + 1 ) ^ { 2 } ( x + 4 )$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { 4 x ^ { 2 } + 8 } { 4 x ^ { 2 } - 8 }$

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } + 3 x + 1$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 1 ) ( x - 8 ) ( x - 1 ) ^ { 2 }$

Graph the polynomial function. - $f ( x ) = 6 x ^ { 3 } - 5 x - x ^ { 5 }$ $Graph the polynomial function. - f ( x ) = 6 x ^ { 3 } - 5 x - x ^ { 5 }$

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

Graph the function. - $f(x)=\frac{x^{2}+4 x+3}{(x-1)^{2}}$ $Graph the function. - f(x)=\frac{x^{2}+4 x+3}{(x-1)^{2}}$

Determine the possible number of positive real zeros and negative real zeros of the polynomial function using Descartes' rule of signs. - $f ( x ) = - 4 x ^ { 7 } - 9 x ^ { 6 } - 4.5 x ^ { 5 } + 3 x ^ { 4 } + x + 18$

Solve the polynomial equation in the complex numbers. - $3 x ^ { 3 } - x ^ { 2 } - 21 x + 7 = 0$

Find the range of the quadratic function in interval notation. - $f ( x ) = - x ^ { 2 } + 14 x + 2$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = x ^ { 2 } + 4 x - 3$

Graph the polynomial function. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$ $Graph the polynomial function. - f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Use the intermediate value theorem to approximate the one real zero on the given interval. Round your answer to two decimal places. - $f ( x ) = x ^ { 3 } - 8 x - 3 ; [ - 3 , - 2 ]$

Find the axis of symmetry of the quadratic function. - $f ( x ) = ( x + 4 ) ^ { 2 } - 6$

Solve the polynomial equation in the complex numbers. - $3 x ^ { 4 } + 20 x ^ { 3 } + 75 x ^ { 2 } + 120 x + 52 = 0$

Solve the polynomial equation in the complex numbers. - $3 x ^ { 4 } - 22 x ^ { 3 } + 64 x ^ { 2 } - 58 x + 13 = 0$

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 2 } - 2 x + 6$