Exam 4: Polynomials and Rational Functions

Solve the problem. Round your answer to two decimal places. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 40 seconds are required to make a 5-by-4 enlargement, find the time required for a 6-by-5 Enlargement.

(Multiple Choice)

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Question 441

Determine whether the statement is true or false. - $f(x)=-\frac{1}{x+1}$ $Determine whether the statement is true or false. - f(x)=-\frac{1}{x+1}$

(Multiple Choice)

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Question 442

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = 2 ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 6 } - 2 \mathrm { x } ^ { 5 } - 4 \mathrm { x } ^ { 4 } + 2 \mathrm { x } ^ { 3 } - 3 \mathrm { x } ^ { 2 } + 3 \mathrm { x } - 5$

(Multiple Choice)

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Question 443

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

(Multiple Choice)

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Question 444

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

(Multiple Choice)

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Question 445

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 446

The graph of $f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x$ is shown below. Use the graph to factor $f ( x )$ . $The graph of f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x is shown below. Use the graph to factor f ( x ) .$

(Multiple Choice)

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Question 447

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - x ^ { 5 } - 3 x ^ { 3 } - 8 x + 1$

(Multiple Choice)

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Question 448

Sketch the graph of the polynomial function. -

(Multiple Choice)

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Question 449

Suppose the cost per ton, $y$ , to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 112,500 } { x + 225 }$ . What is the cost per ton for $x = 100 ?$

(Multiple Choice)

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Question 450

Identify the vertex of the parabola. -Identify the vertex of the parabola $y = 2 x ^ { 2 } + 4 x + 0$

(Multiple Choice)

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Question 451

Solve the problem. Round your answer to two decimal places. -The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 45 miles per hour?

(Multiple Choice)

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Question 452

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22$

(Multiple Choice)

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Question 453

Round to the nearest tenth unless indicated otherwise. -Wind resistance or atmospheric drag tends to slow down moving objects. Atmospheric drag varies jointly as an object's surface area A and velocity v. If a car traveling at a speed of $40 \mathrm { mph }$ with a surface area of $34 \mathrm { ft } ^ { 2 }$ experiences a drag of $231.2 \mathrm {~N}$ (Newtons), how fast must a car with $39 \mathrm { ft } ^ { 2 }$ of surface area travel in order to experience a drag force of $483.99 \mathrm {~N}$ ?

(Multiple Choice)

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Question 454

Translate the given formula to an English phrase using the word "varies". - , where f is the centripetal force of an object of mass m moving along a circle of radius r at velocity v

(Essay)

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Question 455

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 456

The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 5 amperes when the resistance is 888 ohms. What is the current when the resistance is 550 ohms? Round to the Nearest tenth.

(Multiple Choice)

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Question 457

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial f(x) $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$ 4x has no real zero greater than 2.

(Multiple Choice)

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Question 458

In the following formula, f(x) is the minimum number of hours of studying required to attain a test score of x: $f ( x ) = \frac { 0.48 x } { 100.5 - x }$ How many hours of study are needed to score 84?

(Multiple Choice)

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Question 459

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = x ^ { 2 } + 9$

(Multiple Choice)

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Question 460

Showing 441 - 460 of 517

Solve the problem. Round your answer to two decimal places. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 40 seconds are required to make a 5-by-4 enlargement, find the time required for a 6-by-5 Enlargement.

Determine whether the statement is true or false. - $f(x)=-\frac{1}{x+1}$ $Determine whether the statement is true or false. - f(x)=-\frac{1}{x+1}$

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = 2 ; \mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 6 } - 2 \mathrm { x } ^ { 5 } - 4 \mathrm { x } ^ { 4 } + 2 \mathrm { x } ^ { 3 } - 3 \mathrm { x } ^ { 2 } + 3 \mathrm { x } - 5$

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

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

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

The graph of $f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x$ is shown below. Use the graph to factor $f ( x )$ . $The graph of f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x is shown below. Use the graph to factor f ( x ) .$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - x ^ { 5 } - 3 x ^ { 3 } - 8 x + 1$

Sketch the graph of the polynomial function. -

Suppose the cost per ton, $y$ , to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 112,500 } { x + 225 }$ . What is the cost per ton for $x = 100 ?$

Identify the vertex of the parabola. -Identify the vertex of the parabola $y = 2 x ^ { 2 } + 4 x + 0$

Solve the problem. Round your answer to two decimal places. -The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 45 miles per hour?

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22$

Translate the given formula to an English phrase using the word "varies". - , where f is the centripetal force of an object of mass m moving along a circle of radius r at velocity v

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

The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 5 amperes when the resistance is 888 ohms. What is the current when the resistance is 550 ohms? Round to the Nearest tenth.

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial f(x) $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$ 4x has no real zero greater than 2.

In the following formula, f(x) is the minimum number of hours of studying required to attain a test score of x: $f ( x ) = \frac { 0.48 x } { 100.5 - x }$ How many hours of study are needed to score 84?

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = x ^ { 2 } + 9$

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

Solve the problem. Round your answer to two decimal places. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 40 seconds are required to make a 5-by-4 enlargement, find the time required for a 6-by-5 Enlargement.

Determine whether the statement is true or false. - f(x)=−1x+1f(x)=-\frac{1}{x+1}f(x)=−x+11​

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

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

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

The graph of f(x)=−x4+x3+8x2−12xf ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 xf(x)=−x4+x3+8x2−12x is shown below. Use the graph to factor f(x)f ( x )f(x) .

Find the correct end behavior diagram for the given polynomial function. - P(x)=−x5−3x3−8x+1P ( x ) = - x ^ { 5 } - 3 x ^ { 3 } - 8 x + 1P(x)=−x5−3x3−8x+1

Sketch the graph of the polynomial function. -

Suppose the cost per ton, yyy , to build an oil platform of xxx thousand tons is approximated by f(x)=112,500x+225f ( x ) = \frac { 112,500 } { x + 225 }f(x)=x+225112,500​ . What is the cost per ton for x=100?x = 100 ?x=100?

Identify the vertex of the parabola. -Identify the vertex of the parabola y=2x2+4x+0y = 2 x ^ { 2 } + 4 x + 0y=2x2+4x+0

Solve the problem. Round your answer to two decimal places. -The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 45 miles per hour?

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x4−10x3+23x2−10x+22f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22f(x)=x4−10x3+23x2−10x+22

Translate the given formula to an English phrase using the word "varies". - , where f is the centripetal force of an object of mass m moving along a circle of radius r at velocity v

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​

The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 5 amperes when the resistance is 888 ohms. What is the current when the resistance is 550 ohms? Round to the Nearest tenth.

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial f(x) f(x)=x5−5x3+4xf ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 xf(x)=x5−5x3+4x 4x has no real zero greater than 2.

In the following formula, f(x) is the minimum number of hours of studying required to attain a test score of x: f(x)=0.48x100.5−xf ( x ) = \frac { 0.48 x } { 100.5 - x }f(x)=100.5−x0.48x​ How many hours of study are needed to score 84?

Find the equation of the axis of symmetry of the parabola. - f(x)=x2+9f ( x ) = x ^ { 2 } + 9f(x)=x2+9

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

Determine whether the statement is true or false. - $f(x)=-\frac{1}{x+1}$ $Determine whether the statement is true or false. - f(x)=-\frac{1}{x+1}$

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

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

The graph of $f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x$ is shown below. Use the graph to factor $f ( x )$ . $The graph of f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x is shown below. Use the graph to factor f ( x ) .$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - x ^ { 5 } - 3 x ^ { 3 } - 8 x + 1$

Suppose the cost per ton, $y$ , to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 112,500 } { x + 225 }$ . What is the cost per ton for $x = 100 ?$

Identify the vertex of the parabola. -Identify the vertex of the parabola $y = 2 x ^ { 2 } + 4 x + 0$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22$

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

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial f(x) $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$ 4x has no real zero greater than 2.

In the following formula, f(x) is the minimum number of hours of studying required to attain a test score of x: $f ( x ) = \frac { 0.48 x } { 100.5 - x }$ How many hours of study are needed to score 84?

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = x ^ { 2 } + 9$