Exam 4: Polynomial and Rational Functions

Solve the variation problem. -The pressure of a gas varies jointly as the quantity of the gas (measured in moles)and the temperature and inversely as the volume of the gas. Suppose that the pressure of a particular gas is 1116 kiloPascals (kPa)when the quantity is 7 moles , the temperature is 310 Kelvin (K), and the volume is 560 cc. Find the pressure of that gas when the number of moles is 8, the temperature is 340 K, and the volume is 960 cc.

(Multiple Choice)

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Question 201

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 5 } }$

(Multiple Choice)

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Question 202

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = - 2 x ^ { 2 } - 12 x - 27$

(Multiple Choice)

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Question 203

Graph the function. - $f ( x ) = \frac { x ^ { 2 } + 10 x + 25 } { x ^ { 2 } + 3 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } + 10 x + 25 } { x ^ { 2 } + 3 }$

(Multiple Choice)

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Question 204

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 8$

(Multiple Choice)

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Question 205

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f(x)=x^{2}-6 x$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=x^{2}-6 x$

(Multiple Choice)

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Question 206

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } - 8 x$

(Multiple Choice)

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Question 207

Use the intermediate value theorem to approximate the one real zero on the given interval. Round your answer to two decimal places. - $f ( x ) = x ^ { 4 } - x ^ { 3 } - 7 x ^ { 2 } + 5 x + 10 ; [ 2,3 ]$

(Multiple Choice)

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Question 208

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { 4 x - 9 } { x - 2 }$

(Multiple Choice)

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Question 209

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = 3 x ^ { 2 } + 3 x - 9$

(Multiple Choice)

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Question 210

Graph the function using transformations. - $f(x)=3-\frac{1}{(x+6)^{2}}$ $Graph the function using transformations. - f(x)=3-\frac{1}{(x+6)^{2}}$

(Multiple Choice)

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Question 211

Graph the function. - $f(x)=\frac{x}{x^{2}-64}$ $Graph the function. - f(x)=\frac{x}{x^{2}-64}$

(Multiple Choice)

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Question 212

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196 ; x - 14$

(Multiple Choice)

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Question 213

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

(Multiple Choice)

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Question 214

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree: 3 ; zeros: $- 2$ and $3 + i$ .

(Multiple Choice)

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Question 215

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = ( x + 2 ) ^ { 2 } - 4$

(Multiple Choice)

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Question 216

Graph the polynomial function. - $f(x)=x^{3}-4 x^{2}+x+6$ $Graph the polynomial function. - f(x)=x^{3}-4 x^{2}+x+6$

(Multiple Choice)

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Question 217

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = - x ^ { 2 } - \frac { 4 } { 5 } x + 6$

(Multiple Choice)

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Question 218

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

(Multiple Choice)

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Question 219

Sketch the graph of the polynomial function. -

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Question 220

Showing 201 - 220 of 255

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 5 } }$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = - 2 x ^ { 2 } - 12 x - 27$

Graph the function. - $f ( x ) = \frac { x ^ { 2 } + 10 x + 25 } { x ^ { 2 } + 3 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } + 10 x + 25 } { x ^ { 2 } + 3 }$

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 8$

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f(x)=x^{2}-6 x$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=x^{2}-6 x$

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } - 8 x$

Use the intermediate value theorem to approximate the one real zero on the given interval. Round your answer to two decimal places. - $f ( x ) = x ^ { 4 } - x ^ { 3 } - 7 x ^ { 2 } + 5 x + 10 ; [ 2,3 ]$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { 4 x - 9 } { x - 2 }$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = 3 x ^ { 2 } + 3 x - 9$

Graph the function using transformations. - $f(x)=3-\frac{1}{(x+6)^{2}}$ $Graph the function using transformations. - f(x)=3-\frac{1}{(x+6)^{2}}$

Graph the function. - $f(x)=\frac{x}{x^{2}-64}$ $Graph the function. - f(x)=\frac{x}{x^{2}-64}$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196 ; x - 14$

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

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree: 3 ; zeros: $- 2$ and $3 + i$ .

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = ( x + 2 ) ^ { 2 } - 4$

Graph the polynomial function. - $f(x)=x^{3}-4 x^{2}+x+6$ $Graph the polynomial function. - f(x)=x^{3}-4 x^{2}+x+6$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = - x ^ { 2 } - \frac { 4 } { 5 } x + 6$

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

Sketch the graph of the polynomial function. -

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Exam 4: Polynomial and Rational Functions

State whether the function is a polynomial function or not. If it is, give its degree. - f(x)=x4−7x5f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 5 } }f(x)=x5x4−7​

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)=−2x2−12x−27f ( x ) = - 2 x ^ { 2 } - 12 x - 27f(x)=−2x2−12x−27

Graph the function. - f(x)=x2+10x+25x2+3f ( x ) = \frac { x ^ { 2 } + 10 x + 25 } { x ^ { 2 } + 3 }f(x)=x2+3x2+10x+25​

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - f(x)=−2x3+2x2−4x+8f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 8f(x)=−2x3+2x2−4x+8

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=x2−6xf(x)=x^{2}-6 xf(x)=x2−6x

Rewrite the quadratic function in standard form by completing the square. - f(x)=x2−8xf ( x ) = x ^ { 2 } - 8 xf(x)=x2−8x

Use the intermediate value theorem to approximate the one real zero on the given interval. Round your answer to two decimal places. - f(x)=x4−x3−7x2+5x+10;[2,3]f ( x ) = x ^ { 4 } - x ^ { 3 } - 7 x ^ { 2 } + 5 x + 10 ; [ 2,3 ]f(x)=x4−x3−7x2+5x+10;[2,3]

Find the vertical asymptotes, if any, of the graph of the rational function. - f(x)=4x−9x−2f ( x ) = \frac { 4 x - 9 } { x - 2 }f(x)=x−24x−9​

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)=3x2+3x−9f ( x ) = 3 x ^ { 2 } + 3 x - 9f(x)=3x2+3x−9

Graph the function using transformations. - f(x)=3−1(x+6)2f(x)=3-\frac{1}{(x+6)^{2}}f(x)=3−(x+6)21​

Graph the function. - f(x)=xx2−64f(x)=\frac{x}{x^{2}-64}f(x)=x2−64x​

Use the Factor Theorem to determine whether x - c is a factor of f(x). - f(x)=x4−45x2−196;x−14f ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196 ; x - 14f(x)=x4−45x2−196;x−14

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

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree: 3 ; zeros: −2- 2−2 and 3+i3 + i3+i .

Find the y-intercept for the graph of the quadratic function. - f(x)=(x+2)2−4f ( x ) = ( x + 2 ) ^ { 2 } - 4f(x)=(x+2)2−4

Graph the polynomial function. - f(x)=x3−4x2+x+6f(x)=x^{3}-4 x^{2}+x+6f(x)=x3−4x2+x+6

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)=−x2−45x+6f ( x ) = - x ^ { 2 } - \frac { 4 } { 5 } x + 6f(x)=−x2−54​x+6

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

Sketch the graph of the polynomial function. -

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

State whether the function is a polynomial function or not. If it is, give its degree. - $f ( x ) = \frac { x ^ { 4 } - 7 } { x ^ { 5 } }$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = - 2 x ^ { 2 } - 12 x - 27$

Graph the function. - $f ( x ) = \frac { x ^ { 2 } + 10 x + 25 } { x ^ { 2 } + 3 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } + 10 x + 25 } { x ^ { 2 } + 3 }$

Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros. - $f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 8$

Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - $f(x)=x^{2}-6 x$ $Graph the quadratic function using its vertex, axis of symmetry, and intercepts. - f(x)=x^{2}-6 x$

Rewrite the quadratic function in standard form by completing the square. - $f ( x ) = x ^ { 2 } - 8 x$

Use the intermediate value theorem to approximate the one real zero on the given interval. Round your answer to two decimal places. - $f ( x ) = x ^ { 4 } - x ^ { 3 } - 7 x ^ { 2 } + 5 x + 10 ; [ 2,3 ]$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { 4 x - 9 } { x - 2 }$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = 3 x ^ { 2 } + 3 x - 9$

Graph the function using transformations. - $f(x)=3-\frac{1}{(x+6)^{2}}$ $Graph the function using transformations. - f(x)=3-\frac{1}{(x+6)^{2}}$

Graph the function. - $f(x)=\frac{x}{x^{2}-64}$ $Graph the function. - f(x)=\frac{x}{x^{2}-64}$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } - 45 x ^ { 2 } - 196 ; x - 14$

Form a polynomial f(x)with real coefficients having the given degree and zeros. -Degree: 3 ; zeros: $- 2$ and $3 + i$ .

Find the y-intercept for the graph of the quadratic function. - $f ( x ) = ( x + 2 ) ^ { 2 } - 4$

Graph the polynomial function. - $f(x)=x^{3}-4 x^{2}+x+6$ $Graph the polynomial function. - f(x)=x^{3}-4 x^{2}+x+6$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = - x ^ { 2 } - \frac { 4 } { 5 } x + 6$