Exam 4: Polynomial and Rational Functions

Solve the problem. -Consider the quadratic model $h ( t ) = - 16 t ^ { 2 } + 40 t + 50$ for the height (in feet), $h$ , of an object $t$ seconds after the object has been projected straight up into the air. Find the maximum height attained by the object. How much time does it take to fall back to the ground? Assume that it takes the same time for going up and coming down.

(Multiple Choice)

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Question 21

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 2 x ^ { 2 } + 3 x + 10$

(Multiple Choice)

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Question 22

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. - $f ( x ) = \frac { x - 4 } { x ^ { 2 } - 7 x + 12 }$ $For the following rational function, identify the coordinates of all removable discontinuities and sketch the graph. Identify all intercepts and find the equations of all asymptotes. - f ( x ) = \frac { x - 4 } { x ^ { 2 } - 7 x + 12 }$

(Multiple Choice)

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Question 23

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = 2 x ^ { 2 } + 10 x - 48$

(Multiple Choice)

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Question 24

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144 ; x - 6$

(Multiple Choice)

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Question 25

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form. - $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 20 x + 14$

(Multiple Choice)

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Question 26

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

(Multiple Choice)

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Question 27

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = 3 x ^ { 5 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = 3 x ^ { 5 }$

(Multiple Choice)

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Question 28

Find the x- and y-intercepts of f. - $f ( x ) = ( x - 4 ) ^ { 2 } \left( x ^ { 2 } - 25 \right)$

(Multiple Choice)

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Question 29

Use synthetic division to divide f(x)by x - c, and then write f(x)in the form f(x)= (x - c)q(x)+ r. - $f ( x ) = x ^ { 5 } + x ^ { 2 } + 1 ; x - 2$

(Multiple Choice)

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Question 30

Solve the variation problem. -The gravitational attraction between two masses varies inversely as the square of the distance between them. If the force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft apart?

(Multiple Choice)

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Question 31

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

(Multiple Choice)

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Question 32

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } + 6 x - 4$

(Multiple Choice)

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Question 33

Find the range of the quadratic function in interval notation. - $f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 6$

(Multiple Choice)

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Question 34

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

(Multiple Choice)

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Question 35

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = 3 x ^ { 2 } + 10 x + 4 \quad$ Give your answers in exact form.

(Multiple Choice)

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Question 36

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = ( x - 3 ) ^ { 2 } - 9$

(Multiple Choice)

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Question 37

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x + 6 } { x ^ { 2 } - 64 }$

(Multiple Choice)

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Question 38

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. - $f ( x ) = 3 ( x - 2 ) ( x - 6 ) ^ { 4 }$

(Multiple Choice)

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Question 39

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = 7 x ^ { 4 } + 20 x ^ { 3 } - 3 x ^ { 2 } + x - 3 ; x + 3$

(Multiple Choice)

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Question 40

Showing 21 - 40 of 255

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 2 x ^ { 2 } + 3 x + 10$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = 2 x ^ { 2 } + 10 x - 48$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144 ; x - 6$

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form. - $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 20 x + 14$

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

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = 3 x ^ { 5 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = 3 x ^ { 5 }$

Find the x- and y-intercepts of f. - $f ( x ) = ( x - 4 ) ^ { 2 } \left( x ^ { 2 } - 25 \right)$

Use synthetic division to divide f(x)by x - c, and then write f(x)in the form f(x)= (x - c)q(x)+ r. - $f ( x ) = x ^ { 5 } + x ^ { 2 } + 1 ; x - 2$

Solve the variation problem. -The gravitational attraction between two masses varies inversely as the square of the distance between them. If the force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft apart?

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

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } + 6 x - 4$

Find the range of the quadratic function in interval notation. - $f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 6$

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

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = 3 x ^ { 2 } + 10 x + 4 \quad$ Give your answers in exact form.

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = ( x - 3 ) ^ { 2 } - 9$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x + 6 } { x ^ { 2 } - 64 }$

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. - $f ( x ) = 3 ( x - 2 ) ( x - 6 ) ^ { 4 }$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = 7 x ^ { 4 } + 20 x ^ { 3 } - 3 x ^ { 2 } + x - 3 ; x + 3$

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Exam 4: Polynomial and Rational Functions

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=x5−2x2+3x+10f ( x ) = x ^ { 5 } - 2 x ^ { 2 } + 3 x + 10f(x)=x5−2x2+3x+10

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)=x−4x2−7x+12f ( x ) = \frac { x - 4 } { x ^ { 2 } - 7 x + 12 }f(x)=x2−7x+12x−4​

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - f(x)=2x2+10x−48f ( x ) = 2 x ^ { 2 } + 10 x - 48f(x)=2x2+10x−48

Use the Factor Theorem to determine whether x - c is a factor of f(x). - f(x)=x4−32x2−144;x−6f ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144 ; x - 6f(x)=x4−32x2−144;x−6

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form. - f(x)=x3+7x2+20x+14f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 20 x + 14f(x)=x3+7x2+20x+14

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

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x)=3x5f ( x ) = 3 x ^ { 5 }f(x)=3x5

Find the x- and y-intercepts of f. - f(x)=(x−4)2(x2−25)f ( x ) = ( x - 4 ) ^ { 2 } \left( x ^ { 2 } - 25 \right)f(x)=(x−4)2(x2−25)

Use synthetic division to divide f(x)by x - c, and then write f(x)in the form f(x)= (x - c)q(x)+ r. - f(x)=x5+x2+1;x−2f ( x ) = x ^ { 5 } + x ^ { 2 } + 1 ; x - 2f(x)=x5+x2+1;x−2

Solve the variation problem. -The gravitational attraction between two masses varies inversely as the square of the distance between them. If the force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft apart?

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

Rewrite the quadratic function in standard form by completing the square. - f(x)=x2+6x−4f ( x ) = x ^ { 2 } + 6 x - 4f(x)=x2+6x−4

Find the range of the quadratic function in interval notation. - f(x)=−7(x−3)2−6f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 6f(x)=−7(x−3)2−6

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

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - f(x)=3x2+10x+4f ( x ) = 3 x ^ { 2 } + 10 x + 4 \quadf(x)=3x2+10x+4 Give your answers in exact form.

Find the x-intercepts (if any) for the graph of the quadratic function. - f(x)=(x−3)2−9f ( x ) = ( x - 3 ) ^ { 2 } - 9f(x)=(x−3)2−9

Find the vertical asymptotes, if any, of the graph of the rational function. - f(x)=x+6x2−64f ( x ) = \frac { x + 6 } { x ^ { 2 } - 64 }f(x)=x2−64x+6​

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(x−2)(x−6)4f ( x ) = 3 ( x - 2 ) ( x - 6 ) ^ { 4 }f(x)=3(x−2)(x−6)4

Use the Factor Theorem to determine whether x - c is a factor of f(x). - f(x)=7x4+20x3−3x2+x−3;x+3f ( x ) = 7 x ^ { 4 } + 20 x ^ { 3 } - 3 x ^ { 2 } + x - 3 ; x + 3f(x)=7x4+20x3−3x2+x−3;x+3

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

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = x ^ { 5 } - 2 x ^ { 2 } + 3 x + 10$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = 2 x ^ { 2 } + 10 x - 48$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144 ; x - 6$

Find all complex zeros of the polynomial function, and write the polynomial in completely factored form. - $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 20 x + 14$

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

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = 3 x ^ { 5 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = 3 x ^ { 5 }$

Find the x- and y-intercepts of f. - $f ( x ) = ( x - 4 ) ^ { 2 } \left( x ^ { 2 } - 25 \right)$

Use synthetic division to divide f(x)by x - c, and then write f(x)in the form f(x)= (x - c)q(x)+ r. - $f ( x ) = x ^ { 5 } + x ^ { 2 } + 1 ; x - 2$

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } + 6 x - 4$

Find the range of the quadratic function in interval notation. - $f ( x ) = - 7 ( x - 3 ) ^ { 2 } - 6$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = 3 x ^ { 2 } + 10 x + 4 \quad$ Give your answers in exact form.

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = ( x - 3 ) ^ { 2 } - 9$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x + 6 } { x ^ { 2 } - 64 }$

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the x-axis at each zero. - $f ( x ) = 3 ( x - 2 ) ( x - 6 ) ^ { 4 }$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = 7 x ^ { 4 } + 20 x ^ { 3 } - 3 x ^ { 2 } + x - 3 ; x + 3$