Exam 4: Polynomials and Rational Functions

$\text { If } s \text { varies directly as } t ^ { 2 } \text {, and } s = 144 \text { when } t = 4 \text {, find } s \text { when } t \text { is } 3 \text {. }$

(Multiple Choice)

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Question 361

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial f(x) $f ( x ) = x ^ { 4 } - 9 x ^ { 3 } - 22 x ^ { 2 }$ has no real zero greater than 8.

(Multiple Choice)

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Question 362

Determine whether the statement is true or false. - $\text { If } x - 3 \text { is a factor of a polynomial } f ( x ) \text {, then } f ( - 3 ) = 0 \text {. }$

(True/False)

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Question 363

Translate the given formula to an English phrase using the word "varies". - $\mathrm { I } = \mathrm { PRT }$ where I is the simple interest on a principal of P dollars invested for T years at an interest rate of R per year

(Essay)

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Question 364

Match the equation to the correct graph $y = ( x - 3 ) ^ { 2 }$

(Multiple Choice)

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Question 365

The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 20 ft from the light.

(Multiple Choice)

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Question 366

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { - 4 } { x ^ { 2 } } \text { is symmetrical with respect to the } y \text {-axis. }$

(True/False)

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Question 367

A rectangular piece of cardboard measuring 17 inches by 30 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. For what value of x will the volume be a maximum? If necessary, round to 2 decimal places.

(Multiple Choice)

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Question 368

Match the equation to the correct graph. - $y = x ^ { 2 } - 2$

(Multiple Choice)

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Question 369

$\text { If } y \text { varies directly as } x ^ { 2 } \text { and inversely as } m \text {, and } y = 4 \text { when } x = 5 \text { and } m = 2 , \text { find } y \text { when } x = 10 \text { and } m = 6 \text {. }$

(Multiple Choice)

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Question 370

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $7 x ^ { 3 } + 18 x ^ { 2 } - 8 x + 3 ; x + 3$

(True/False)

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Question 371

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { 2 x - 4 } { x ^ { 2 } + 6 x - 27 }$

(Multiple Choice)

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Question 372

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$

(Multiple Choice)

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Question 373

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 374

If m varies directly as p, a $m = 20 \text { when } p = 4$ , find m when p is 8.

(Multiple Choice)

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Question 375

Find a polynomial of least degree with only real coefficients and having the given zeros. - $- \sqrt { 3 } , \sqrt { 3 }$ , and 8 (multiplicity 2 )

(Multiple Choice)

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Question 376

Find an equation for the rational function graph. -

(Multiple Choice)

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Question 377

Solve the problem. Round your answer to two decimal places. -The weight W of an object on the Moon varies directly as the weight E on earth. A person who weighs 136 lb on earth weighs 27.2 lb on the Moon. How much would a 124-lb person weigh on the Moon?

(Multiple Choice)

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Question 378

A 13 m by 17 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 621 m2?

(Multiple Choice)

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Question 379

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

(True/False)

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Question 380

$\text { If } s \text { varies directly as } t ^ { 2 } \text {, and } s = 144 \text { when } t = 4 \text {, find } s \text { when } t \text { is } 3 \text {. }$

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial f(x) $f ( x ) = x ^ { 4 } - 9 x ^ { 3 } - 22 x ^ { 2 }$ has no real zero greater than 8.

Determine whether the statement is true or false. - $\text { If } x - 3 \text { is a factor of a polynomial } f ( x ) \text {, then } f ( - 3 ) = 0 \text {. }$

Translate the given formula to an English phrase using the word "varies". - $\mathrm { I } = \mathrm { PRT }$ where I is the simple interest on a principal of P dollars invested for T years at an interest rate of R per year

Match the equation to the correct graph $y = ( x - 3 ) ^ { 2 }$

The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 20 ft from the light.

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { - 4 } { x ^ { 2 } } \text { is symmetrical with respect to the } y \text {-axis. }$

Match the equation to the correct graph. - $y = x ^ { 2 } - 2$

$\text { If } y \text { varies directly as } x ^ { 2 } \text { and inversely as } m \text {, and } y = 4 \text { when } x = 5 \text { and } m = 2 , \text { find } y \text { when } x = 10 \text { and } m = 6 \text {. }$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $7 x ^ { 3 } + 18 x ^ { 2 } - 8 x + 3 ; x + 3$

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { 2 x - 4 } { x ^ { 2 } + 6 x - 27 }$

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$

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

If m varies directly as p, a $m = 20 \text { when } p = 4$ , find m when p is 8.

Find a polynomial of least degree with only real coefficients and having the given zeros. - $- \sqrt { 3 } , \sqrt { 3 }$ , and 8 (multiplicity 2 )

Find an equation for the rational function graph. -

Solve the problem. Round your answer to two decimal places. -The weight W of an object on the Moon varies directly as the weight E on earth. A person who weighs 136 lb on earth weighs 27.2 lb on the Moon. How much would a 124-lb person weigh on the Moon?

A 13 m by 17 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 621 m2?

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

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

If s varies directly as t2, and s=144 when t=4, find s when t is 3. \text { If } s \text { varies directly as } t ^ { 2 } \text {, and } s = 144 \text { when } t = 4 \text {, find } s \text { when } t \text { is } 3 \text {. } If s varies directly as t2, and s=144 when t=4, find s when t is 3.

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial f(x) f(x)=x4−9x3−22x2f ( x ) = x ^ { 4 } - 9 x ^ { 3 } - 22 x ^ { 2 }f(x)=x4−9x3−22x2 has no real zero greater than 8.

Determine whether the statement is true or false. - If x−3 is a factor of a polynomial f(x), then f(−3)=0. \text { If } x - 3 \text { is a factor of a polynomial } f ( x ) \text {, then } f ( - 3 ) = 0 \text {. } If x−3 is a factor of a polynomial f(x), then f(−3)=0.

Translate the given formula to an English phrase using the word "varies". - I=PRT\mathrm { I } = \mathrm { PRT }I=PRT where I is the simple interest on a principal of P dollars invested for T years at an interest rate of R per year

Match the equation to the correct graph y=(x−3)2y = ( x - 3 ) ^ { 2 }y=(x−3)2

The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 20 ft from the light.

Match the equation to the correct graph. - y=x2−2y = x ^ { 2 } - 2y=x2−2

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - 7x3+18x2−8x+3;x+37 x ^ { 3 } + 18 x ^ { 2 } - 8 x + 3 ; x + 37x3+18x2−8x+3;x+3

Give the equations of any vertical asymptotes. - h(x)=2x−4x2+6x−27h ( x ) = \frac { 2 x - 4 } { x ^ { 2 } + 6 x - 27 }h(x)=x2+6x−272x−4​

Find all rational zeros and factor f(x). - f(x)=x3−8x2−x+8f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8f(x)=x3−8x2−x+8

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

If m varies directly as p, a m=20 when p=4m = 20 \text { when } p = 4m=20 when p=4 , find m when p is 8.

Find a polynomial of least degree with only real coefficients and having the given zeros. - −3,3- \sqrt { 3 } , \sqrt { 3 }−3​,3​ , and 8 (multiplicity 2 )

Find an equation for the rational function graph. -

Solve the problem. Round your answer to two decimal places. -The weight W of an object on the Moon varies directly as the weight E on earth. A person who weighs 136 lb on earth weighs 27.2 lb on the Moon. How much would a 124-lb person weigh on the Moon?

A 13 m by 17 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 621 m2?

Determine whether the statement is true or false. - The function f(x)=1x is decreasing on the interval (−∞,∞)\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( - \infty , \infty ) The function f(x)=x1​ is decreasing on the interval (−∞,∞)

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

$\text { If } s \text { varies directly as } t ^ { 2 } \text {, and } s = 144 \text { when } t = 4 \text {, find } s \text { when } t \text { is } 3 \text {. }$

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial f(x) $f ( x ) = x ^ { 4 } - 9 x ^ { 3 } - 22 x ^ { 2 }$ has no real zero greater than 8.

Determine whether the statement is true or false. - $\text { If } x - 3 \text { is a factor of a polynomial } f ( x ) \text {, then } f ( - 3 ) = 0 \text {. }$

Translate the given formula to an English phrase using the word "varies". - $\mathrm { I } = \mathrm { PRT }$ where I is the simple interest on a principal of P dollars invested for T years at an interest rate of R per year

Match the equation to the correct graph $y = ( x - 3 ) ^ { 2 }$

Match the equation to the correct graph. - $y = x ^ { 2 } - 2$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $7 x ^ { 3 } + 18 x ^ { 2 } - 8 x + 3 ; x + 3$

Give the equations of any vertical asymptotes. - $h ( x ) = \frac { 2 x - 4 } { x ^ { 2 } + 6 x - 27 }$

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x + 8$

If m varies directly as p, a $m = 20 \text { when } p = 4$ , find m when p is 8.

Find a polynomial of least degree with only real coefficients and having the given zeros. - $- \sqrt { 3 } , \sqrt { 3 }$ , and 8 (multiplicity 2 )

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