Exam 3: Polynomial and Rational Functions

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-4)^{2}-1$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-4)^{2}-1 Find the equation of the axis.$ Find the equation of the axis.

(Multiple Choice)

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Question 381

Find an equation for the rational function graph. -

(Multiple Choice)

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Question 382

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a>0;-4ac<0

(Multiple Choice)

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Question 383

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = 4 + 3 \mathrm { i } ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 5 \mathrm { x } - 3$

(Multiple Choice)

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Question 384

Identify the vertex of the parabola. - $\mathrm { y } = \mathrm { x } ^ { 2 } + 1$

(Multiple Choice)

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Question 385

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = - 2 x ^ { 3 } - 16 x ^ { 2 } + 30 x + 108 ; [ 0,1 ]$

(Multiple Choice)

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Question 386

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 1 } { x ^ { 2 } } \text { is increasing on the interval } ( - \infty , 0 )$

(True/False)

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Question 387

Solve the problem. - $\text { If the average cost per unit } C ( x ) \text { to produce } x \text { units of plywood is given by } C ( x ) = \frac { 600 } { x + 20 } \text {, what do }$

(Multiple Choice)

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Question 388

Solve the problem. -The graph of $f ( x ) = x ^ { 4 } + x ^ { 3 } - 6 x ^ { 2 } - x ^ { 2 } - x + 6$ is shown below. Use the graph to factor $f ( x )$ . $Solve the problem. -The graph of f ( x ) = x ^ { 4 } + x ^ { 3 } - 6 x ^ { 2 } - x ^ { 2 } - x + 6 is shown below. Use the graph to factor f ( x ) .$

(Multiple Choice)

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Question 389

Sketch the graph of the rational function. - $f ( x ) = \frac { x + 1 } { x ^ { 2 } + x - 12 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x + 1 } { x ^ { 2 } + x - 12 }$

(Multiple Choice)

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Question 390

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

(Multiple Choice)

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Question 391

Solve the problem. -A rectangular piece of cardboard measuring 29 inches by 50 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let $x$ represent the length of a side of each such square. What is the maximum volume of this box? If necessary, round to 2 decimal places.

(Multiple Choice)

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Question 392

Find an equation for the rational function graph. -

(Multiple Choice)

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Question 393

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $2 ; f ( x ) = 9 x ^ { 3 } - 4 x ^ { 2 } + x - 58$

(Multiple Choice)

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Question 394

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$ has no real zero greater than 2 .

(True/False)

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Question 395

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x - 6$

(Multiple Choice)

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Question 396

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

(Multiple Choice)

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Question 397

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $6 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

(Multiple Choice)

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Question 398

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - $2 x ^ { 6 } - 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } - 3 x = 0$

(Multiple Choice)

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Question 399

Solve the problem. -A $19 \mathrm {~m}$ by $24 \mathrm {~m}$ rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $864 \mathrm {~m} ^ { 2 }$ ?

(Multiple Choice)

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Question 400

Find an equation for the rational function graph. -

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a>0;-4ac<0

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = 4 + 3 \mathrm { i } ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 5 \mathrm { x } - 3$

Identify the vertex of the parabola. - $\mathrm { y } = \mathrm { x } ^ { 2 } + 1$

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = - 2 x ^ { 3 } - 16 x ^ { 2 } + 30 x + 108 ; [ 0,1 ]$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 1 } { x ^ { 2 } } \text { is increasing on the interval } ( - \infty , 0 )$

Solve the problem. - $\text { If the average cost per unit } C ( x ) \text { to produce } x \text { units of plywood is given by } C ( x ) = \frac { 600 } { x + 20 } \text {, what do }$

Sketch the graph of the rational function. - $f ( x ) = \frac { x + 1 } { x ^ { 2 } + x - 12 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x + 1 } { x ^ { 2 } + x - 12 }$

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

Find an equation for the rational function graph. -

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $2 ; f ( x ) = 9 x ^ { 3 } - 4 x ^ { 2 } + x - 58$

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$ has no real zero greater than 2 .

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x - 6$

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $6 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - $2 x ^ { 6 } - 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } - 3 x = 0$

Solve the problem. -A $19 \mathrm {~m}$ by $24 \mathrm {~m}$ rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $864 \mathrm {~m} ^ { 2 }$ ?

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 3: Polynomial and Rational Functions

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−4)2−1f(x)=(x-4)^{2}-1f(x)=(x−4)2−1 Find the equation of the axis.

Find an equation for the rational function graph. -

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a>0;-4ac<0

Use the remainder theorem and synthetic division to find f(k). - k=4+3i;f(x)=x2−5x−3\mathrm { k } = 4 + 3 \mathrm { i } ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 5 \mathrm { x } - 3k=4+3i;f(x)=x2−5x−3

Identify the vertex of the parabola. - y=x2+1\mathrm { y } = \mathrm { x } ^ { 2 } + 1y=x2+1

Determine whether the statement is true or false. - The function f(x)=1x2 is increasing on the interval (−∞,0)\text { The function } f ( x ) = \frac { 1 } { x ^ { 2 } } \text { is increasing on the interval } ( - \infty , 0 ) The function f(x)=x21​ is increasing on the interval (−∞,0)

Solve the problem. -The graph of f(x)=x4+x3−6x2−x2−x+6f ( x ) = x ^ { 4 } + x ^ { 3 } - 6 x ^ { 2 } - x ^ { 2 } - x + 6f(x)=x4+x3−6x2−x2−x+6 is shown below. Use the graph to factor f(x)f ( x )f(x) .

Sketch the graph of the rational function. - f(x)=x+1x2+x−12f ( x ) = \frac { x + 1 } { x ^ { 2 } + x - 12 }f(x)=x2+x−12x+1​

Sketch the graph of the rational function. - f(x)=x2+3x−42x2+1f ( x ) = \frac { x ^ { 2 } + 3 x - 4 } { 2 x ^ { 2 } + 1 }f(x)=2x2+1x2+3x−4​

Find an equation for the rational function graph. -

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - 2;f(x)=9x3−4x2+x−582 ; f ( x ) = 9 x ^ { 3 } - 4 x ^ { 2 } + x - 582;f(x)=9x3−4x2+x−58

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial f(x)=x5−5x3+4xf ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 xf(x)=x5−5x3+4x has no real zero greater than 2 .

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - f(x)=x3+2x2−3x−6f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x - 6f(x)=x3+2x2−3x−6

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - 6x4+13x3−2x2+x+4;x+26 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 26x4+13x3−2x2+x+4;x+2

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - 2x6−3x4−8x3+6x2−3x=02 x ^ { 6 } - 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } - 3 x = 02x6−3x4−8x3+6x2−3x=0

Solve the problem. -A 19 m19 \mathrm {~m}19 m by 24 m24 \mathrm {~m}24 m rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 864 m2864 \mathrm {~m} ^ { 2 }864 m2 ?

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = 4 + 3 \mathrm { i } ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 5 \mathrm { x } - 3$

Identify the vertex of the parabola. - $\mathrm { y } = \mathrm { x } ^ { 2 } + 1$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 1 } { x ^ { 2 } } \text { is increasing on the interval } ( - \infty , 0 )$

Sketch the graph of the rational function. - $f ( x ) = \frac { x + 1 } { x ^ { 2 } + x - 12 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x + 1 } { x ^ { 2 } + x - 12 }$

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

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $2 ; f ( x ) = 9 x ^ { 3 } - 4 x ^ { 2 } + x - 58$

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$ has no real zero greater than 2 .

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x - 6$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $6 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - $2 x ^ { 6 } - 3 x ^ { 4 } - 8 x ^ { 3 } + 6 x ^ { 2 } - 3 x = 0$

Solve the problem. -A $19 \mathrm {~m}$ by $24 \mathrm {~m}$ rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $864 \mathrm {~m} ^ { 2 }$ ?