Exam 4: Polynomials and Rational Functions

Use synthetic division $f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$ for the given value of k. - $f ( x ) = 3 x ^ { 3 } - x ^ { 2 } + 2 x + 3 ; k = - 1$

(Multiple Choice)

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Question 381

Identify the vertex of the parabola. -Identify the vertex of the parabola. $y = 3 x ^ { 2 } - 6 x - 2$

(Multiple Choice)

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Question 382

Sketch the graph of the polynomial function. -

(Multiple Choice)

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Question 383

Determine which of the rational functions given below has the following feature(s). -The vertical asymptote is $x = 4$

(Multiple Choice)

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Question 384

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-1)^{2}+3$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-1)^{2}+3 Find the \mathrm { y } -intercept.$ Find the $\mathrm { y }$ -intercept.

(Multiple Choice)

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Question 385

Find an equation for the rational function graph. -

(Multiple Choice)

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Question 386

Find an equation for the rational function graph. -

(Multiple Choice)

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Question 387

Use the graph to answer the question. -Find the domain of the rational function graphed below.

(Multiple Choice)

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Question 388

If the average cost per unit C(x) to produce x units of plywood is given by C(x) = x 600+ 20, what do 600 units cost?

(Multiple Choice)

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Question 389

Suppose the cost per ton, $f ( x )$ , to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 162,500 } { x + 325 }$ . What is the cost per ton for $x = 50 ?$

(Multiple Choice)

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Question 390

Find the zeros of the polynomial function and state the multiplicity of each. $f ( x ) = ( 7 x - 2 ) ^ { 4 } \left( x ^ { 2 } + 16 \right) ^ { 3 }$

(Multiple Choice)

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Question 391

Sketch the graph of the polynomial function. -

(Multiple Choice)

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Question 392

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-1)^{2}+2$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-1)^{2}+2 Find the x -intercepts.$ Find the $x$ -intercepts.

(Multiple Choice)

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Question 393

A quadratic equation f(x)=0 has a solution x=3 . Its graph has vertex (-1,-16) . What is the other solution of the equation?

(Multiple Choice)

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Question 394

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-3)^{2}+4$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-3)^{2}+4 Find the coordinates of the vertex.$ Find the coordinates of the vertex.

(Multiple Choice)

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Question 395

If y varies inversely as x, and x is halved, how is y changed?

(Multiple Choice)

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Question 396

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

(Multiple Choice)

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Question 397

Translate the given formula to an English phrase using the word "varies". - $\mathrm { P } = \mathrm { nb }$ b, where P is the perimeter of a regular polygon with n sides each of length b.

(Essay)

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Question 398

$\text { How can the graph of } f ( x ) = \frac { 1 } { x - 6 } \text { be obtained from the graph of } y = \frac { 1 } { x } \text { ? }$

(Multiple Choice)

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Question 399

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative. - $Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of x ^ { 2 } should be positive or negative. -$

(Multiple Choice)

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Question 400

Showing 381 - 400 of 517

Use synthetic division $f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$ for the given value of k. - $f ( x ) = 3 x ^ { 3 } - x ^ { 2 } + 2 x + 3 ; k = - 1$

Identify the vertex of the parabola. -Identify the vertex of the parabola. $y = 3 x ^ { 2 } - 6 x - 2$

Sketch the graph of the polynomial function. -

Determine which of the rational functions given below has the following feature(s). -The vertical asymptote is $x = 4$

Find an equation for the rational function graph. -

Find an equation for the rational function graph. -

Use the graph to answer the question. -Find the domain of the rational function graphed below.

If the average cost per unit C(x) to produce x units of plywood is given by C(x) = x 600+ 20, what do 600 units cost?

Suppose the cost per ton, $f ( x )$ , to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 162,500 } { x + 325 }$ . What is the cost per ton for $x = 50 ?$

Find the zeros of the polynomial function and state the multiplicity of each. $f ( x ) = ( 7 x - 2 ) ^ { 4 } \left( x ^ { 2 } + 16 \right) ^ { 3 }$

Sketch the graph of the polynomial function. -

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-1)^{2}+2$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-1)^{2}+2 Find the x -intercepts.$ Find the $x$ -intercepts.

A quadratic equation f(x)=0 has a solution x=3 . Its graph has vertex (-1,-16) . What is the other solution of the equation?

If y varies inversely as x, and x is halved, how is y changed?

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Translate the given formula to an English phrase using the word "varies". - $\mathrm { P } = \mathrm { nb }$ b, where P is the perimeter of a regular polygon with n sides each of length b.

$\text { How can the graph of } f ( x ) = \frac { 1 } { x - 6 } \text { be obtained from the graph of } y = \frac { 1 } { x } \text { ? }$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 4: Polynomials and Rational Functions

Identify the vertex of the parabola. -Identify the vertex of the parabola. y=3x2−6x−2y = 3 x ^ { 2 } - 6 x - 2y=3x2−6x−2

Sketch the graph of the polynomial function. -

Determine which of the rational functions given below has the following feature(s). -The vertical asymptote is x=4x = 4x=4

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=−2(x−1)2+3f(x)=-2(x-1)^{2}+3f(x)=−2(x−1)2+3 Find the y\mathrm { y }y -intercept.

Find an equation for the rational function graph. -

Find an equation for the rational function graph. -

Use the graph to answer the question. -Find the domain of the rational function graphed below.

If the average cost per unit C(x) to produce x units of plywood is given by C(x) = x 600+ 20, what do 600 units cost?

Suppose the cost per ton, f(x)f ( x )f(x) , to build an oil platform of xxx thousand tons is approximated by f(x)=162,500x+325f ( x ) = \frac { 162,500 } { x + 325 }f(x)=x+325162,500​ . What is the cost per ton for x=50?x = 50 ?x=50?

Find the zeros of the polynomial function and state the multiplicity of each. f(x)=(7x−2)4(x2+16)3f ( x ) = ( 7 x - 2 ) ^ { 4 } \left( x ^ { 2 } + 16 \right) ^ { 3 }f(x)=(7x−2)4(x2+16)3

Sketch the graph of the polynomial function. -

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=−2(x−1)2+2f(x)=-2(x-1)^{2}+2f(x)=−2(x−1)2+2 Find the xxx -intercepts.

A quadratic equation f(x)=0 has a solution x=3 . Its graph has vertex (-1,-16) . What is the other solution of the equation?

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=−2(x−3)2+4f(x)=-2(x-3)^{2}+4f(x)=−2(x−3)2+4 Find the coordinates of the vertex.

If y varies inversely as x, and x is halved, how is y changed?

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Translate the given formula to an English phrase using the word "varies". - P=nb\mathrm { P } = \mathrm { nb }P=nb b, where P is the perimeter of a regular polygon with n sides each of length b.

How can the graph of f(x)=1x−6 be obtained from the graph of y=1x ? \text { How can the graph of } f ( x ) = \frac { 1 } { x - 6 } \text { be obtained from the graph of } y = \frac { 1 } { x } \text { ? } How can the graph of f(x)=x−61​ be obtained from the graph of y=x1​ ?

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of x2x ^ { 2 }x2 should be positive or negative. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Identify the vertex of the parabola. -Identify the vertex of the parabola. $y = 3 x ^ { 2 } - 6 x - 2$

Determine which of the rational functions given below has the following feature(s). -The vertical asymptote is $x = 4$

Suppose the cost per ton, $f ( x )$ , to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 162,500 } { x + 325 }$ . What is the cost per ton for $x = 50 ?$

Find the zeros of the polynomial function and state the multiplicity of each. $f ( x ) = ( 7 x - 2 ) ^ { 4 } \left( x ^ { 2 } + 16 \right) ^ { 3 }$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-1)^{2}+2$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-1)^{2}+2 Find the x -intercepts.$ Find the $x$ -intercepts.

Translate the given formula to an English phrase using the word "varies". - $\mathrm { P } = \mathrm { nb }$ b, where P is the perimeter of a regular polygon with n sides each of length b.

$\text { How can the graph of } f ( x ) = \frac { 1 } { x - 6 } \text { be obtained from the graph of } y = \frac { 1 } { x } \text { ? }$