Exam 4: Polynomials and Rational Functions

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-1)^{2}-3$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-1)^{2}-3 Find the coordinates of the vertex.$ Find the coordinates of the vertex.

(Multiple Choice)

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Question 321

The student population of a small school has been increasing as shown in the following table. Determine the linear, quadratic, or cubic function that best fits the data.

(Multiple Choice)

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Question 322

Solve the problem. Round your answer to two decimal places. -According to Ohm's law, the electric current I, in amperes, in a circuit varies directly as the voltage V. When 28 volts are applied, the current is 4 amperes. What is the current when 10 volts are applied?

(Multiple Choice)

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Question 323

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = - 2 ; \mathrm { f } ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } - 4 \mathrm { x } ^ { 2 } - 3 \mathrm { x } + 24$

(Multiple Choice)

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Question 324

Sketch the graph of the rational function. - $f ( x ) = \frac { x ( x + 5 ) } { ( x + 4 ) ^ { 2 } }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ( x + 5 ) } { ( x + 4 ) ^ { 2 } }$

(Multiple Choice)

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Question 325

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 326

Identify the vertex of the parabola. -Identify the vertex of the parabola $y = 3 x ^ { 2 } - 6 x + 0$

(Multiple Choice)

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Question 327

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

(Multiple Choice)

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Question 328

Determine whether the statement is true or false. - $f(x)=2-\frac{2}{x}$ $Determine whether the statement is true or false. - f(x)=2-\frac{2}{x}$

(Multiple Choice)

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Question 329

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 10 x ^ { 5 } + 3 x ^ { 3 } - 3 x ^ { 2 } + 6 ; - 1$ and 0

(Multiple Choice)

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Question 330

What type of variation is suggested by the graph?

(Multiple Choice)

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Question 331

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. - $f ( x ) = - x ^ { 4 } + 29 x ^ { 2 } - 100 ; [ 3,4 ]$

(Multiple Choice)

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Question 332

Factor f(x) into linear factors given that k is a zero of f(x). $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 7 x ^ { 2 } - 12 x - 18$ k= -3 (multiplicity 2)

(Multiple Choice)

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Question 333

Give all possible rational zeros for the following polynomial $P ( x ) = 5 x ^ { 3 } + 7 x ^ { 2 } + 2 x - 10$

(Multiple Choice)

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Question 334

Match the equation to the correct graph $y = 2 ( x - 4 ) ^ { 2 } - 3$

(Multiple Choice)

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Question 335

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 8 x - 14 \geq 0$

(Multiple Choice)

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Question 336

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = 3 x ^ { 4 } - 10 x ^ { 3 } + 20 x ^ { 2 } - 40 x + 32$

(Multiple Choice)

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Question 337

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

(True/False)

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Question 338

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 5 x ( x + 6 ) \left( x ^ { 2 } - 1 \right) ^ { 3 }$

(Multiple Choice)

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Question 339

$A ( x ) = - 0.015 x ^ { 3 } + 1.05 x$ gives the alcohol level in an average person's blood $x$ hrs after drinking 8 oz of 100 - proof whiskey. If the level exceeds $1.5$ units, a person is legally drunk. Would a person be drunk after 3 hours?

(True/False)

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Question 340

The student population of a small school has been increasing as shown in the following table. Determine the linear, quadratic, or cubic function that best fits the data.

Solve the problem. Round your answer to two decimal places. -According to Ohm's law, the electric current I, in amperes, in a circuit varies directly as the voltage V. When 28 volts are applied, the current is 4 amperes. What is the current when 10 volts are applied?

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = - 2 ; \mathrm { f } ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } - 4 \mathrm { x } ^ { 2 } - 3 \mathrm { x } + 24$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ( x + 5 ) } { ( x + 4 ) ^ { 2 } }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ( x + 5 ) } { ( x + 4 ) ^ { 2 } }$

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

Identify the vertex of the parabola. -Identify the vertex of the parabola $y = 3 x ^ { 2 } - 6 x + 0$

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

Determine whether the statement is true or false. - $f(x)=2-\frac{2}{x}$ $Determine whether the statement is true or false. - f(x)=2-\frac{2}{x}$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 10 x ^ { 5 } + 3 x ^ { 3 } - 3 x ^ { 2 } + 6 ; - 1$ and 0

What type of variation is suggested by the graph?

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. - $f ( x ) = - x ^ { 4 } + 29 x ^ { 2 } - 100 ; [ 3,4 ]$

Factor f(x) into linear factors given that k is a zero of f(x). $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 7 x ^ { 2 } - 12 x - 18$ k= -3 (multiplicity 2)

Give all possible rational zeros for the following polynomial $P ( x ) = 5 x ^ { 3 } + 7 x ^ { 2 } + 2 x - 10$

Match the equation to the correct graph $y = 2 ( x - 4 ) ^ { 2 } - 3$

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 8 x - 14 \geq 0$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = 3 x ^ { 4 } - 10 x ^ { 3 } + 20 x ^ { 2 } - 40 x + 32$

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

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 5 x ( x + 6 ) \left( x ^ { 2 } - 1 \right) ^ { 3 }$

$A ( x ) = - 0.015 x ^ { 3 } + 1.05 x$ gives the alcohol level in an average person's blood $x$ hrs after drinking 8 oz of 100 - proof whiskey. If the level exceeds $1.5$ units, a person is legally drunk. Would a person be drunk after 3 hours?

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

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−1)2−3f(x)=(x-1)^{2}-3f(x)=(x−1)2−3 Find the coordinates of the vertex.

The student population of a small school has been increasing as shown in the following table. Determine the linear, quadratic, or cubic function that best fits the data.

Solve the problem. Round your answer to two decimal places. -According to Ohm's law, the electric current I, in amperes, in a circuit varies directly as the voltage V. When 28 volts are applied, the current is 4 amperes. What is the current when 10 volts are applied?

Use the remainder theorem and synthetic division to find f(k). - k=−2;f(x)=2x3−4x2−3x+24\mathrm { k } = - 2 ; \mathrm { f } ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } - 4 \mathrm { x } ^ { 2 } - 3 \mathrm { x } + 24k=−2;f(x)=2x3−4x2−3x+24

Sketch the graph of the rational function. - f(x)=x(x+5)(x+4)2f ( x ) = \frac { x ( x + 5 ) } { ( x + 4 ) ^ { 2 } }f(x)=(x+4)2x(x+5)​

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

Identify the vertex of the parabola. -Identify the vertex of the parabola y=3x2−6x+0y = 3 x ^ { 2 } - 6 x + 0y=3x2−6x+0

Use the remainder theorem and synthetic division to find f(k). - k=2;f(x)=−x3−2x2+4\mathrm { k } = 2 ; \mathrm { f } ( \mathrm { x } ) = - \mathrm { x } ^ { 3 } - 2 \mathrm { x } ^ { 2 } + 4k=2;f(x)=−x3−2x2+4

Determine whether the statement is true or false. - f(x)=2−2xf(x)=2-\frac{2}{x}f(x)=2−x2​

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - f(x)=10x5+3x3−3x2+6;−1f ( x ) = 10 x ^ { 5 } + 3 x ^ { 3 } - 3 x ^ { 2 } + 6 ; - 1f(x)=10x5+3x3−3x2+6;−1 and 0

What type of variation is suggested by the graph?

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)=−x4+29x2−100;[3,4]f ( x ) = - x ^ { 4 } + 29 x ^ { 2 } - 100 ; [ 3,4 ]f(x)=−x4+29x2−100;[3,4]

Factor f(x) into linear factors given that k is a zero of f(x). f(x)=x4+6x3+7x2−12x−18f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 7 x ^ { 2 } - 12 x - 18f(x)=x4+6x3+7x2−12x−18 k= -3 (multiplicity 2)

Give all possible rational zeros for the following polynomial P(x)=5x3+7x2+2x−10P ( x ) = 5 x ^ { 3 } + 7 x ^ { 2 } + 2 x - 10P(x)=5x3+7x2+2x−10

Match the equation to the correct graph y=2(x−4)2−3y = 2 ( x - 4 ) ^ { 2 } - 3y=2(x−4)2−3

Solve the inequality. Write the solution set in interval notation. - −x2+8x−14≥0- x ^ { 2 } + 8 x - 14 \geq 0−x2+8x−14≥0

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=3x4−10x3+20x2−40x+32f ( x ) = 3 x ^ { 4 } - 10 x ^ { 3 } + 20 x ^ { 2 } - 40 x + 32f(x)=3x4−10x3+20x2−40x+32

Find the zeros of the polynomial function and state the multiplicity of each. - f(x)=5x(x+6)(x2−1)3f ( x ) = 5 x ( x + 6 ) \left( x ^ { 2 } - 1 \right) ^ { 3 }f(x)=5x(x+6)(x2−1)3

A(x)=−0.015x3+1.05xA ( x ) = - 0.015 x ^ { 3 } + 1.05 xA(x)=−0.015x3+1.05x gives the alcohol level in an average person's blood xxx hrs after drinking 8 oz of 100 - proof whiskey. If the level exceeds 1.51.51.5 units, a person is legally drunk. Would a person be drunk after 3 hours?

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

Use the remainder theorem and synthetic division to find f(k). - $\mathrm { k } = - 2 ; \mathrm { f } ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } - 4 \mathrm { x } ^ { 2 } - 3 \mathrm { x } + 24$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ( x + 5 ) } { ( x + 4 ) ^ { 2 } }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ( x + 5 ) } { ( x + 4 ) ^ { 2 } }$

Identify the vertex of the parabola. -Identify the vertex of the parabola $y = 3 x ^ { 2 } - 6 x + 0$

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

Determine whether the statement is true or false. - $f(x)=2-\frac{2}{x}$ $Determine whether the statement is true or false. - f(x)=2-\frac{2}{x}$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 10 x ^ { 5 } + 3 x ^ { 3 } - 3 x ^ { 2 } + 6 ; - 1$ and 0

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. - $f ( x ) = - x ^ { 4 } + 29 x ^ { 2 } - 100 ; [ 3,4 ]$

Factor f(x) into linear factors given that k is a zero of f(x). $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 7 x ^ { 2 } - 12 x - 18$ k= -3 (multiplicity 2)

Give all possible rational zeros for the following polynomial $P ( x ) = 5 x ^ { 3 } + 7 x ^ { 2 } + 2 x - 10$

Match the equation to the correct graph $y = 2 ( x - 4 ) ^ { 2 } - 3$

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 8 x - 14 \geq 0$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = 3 x ^ { 4 } - 10 x ^ { 3 } + 20 x ^ { 2 } - 40 x + 32$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 5 x ( x + 6 ) \left( x ^ { 2 } - 1 \right) ^ { 3 }$

$A ( x ) = - 0.015 x ^ { 3 } + 1.05 x$ gives the alcohol level in an average person's blood $x$ hrs after drinking 8 oz of 100 - proof whiskey. If the level exceeds $1.5$ units, a person is legally drunk. Would a person be drunk after 3 hours?