Exam 2: Polynomial, Power, and Rational Functions

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - $f ( x ) = - 2.8 x ^ { 6 }$

(Multiple Choice)

4.9/5

(41)

Question 441

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 8 x - 2 ; d ( x ) = x + 4 \quad$ (Write answer in polynomial form)

(Multiple Choice)

4.8/5

(37)

Question 442

Solve the problem. -Find the remainder when $x ^ { 43 } + 18$ is divided by $x - 1$ .

(Multiple Choice)

4.8/5

(29)

Question 443

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 5 x - 10$ - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 5 x - 10$

(Multiple Choice)

4.8/5

(46)

Question 444

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 2 ( x + 9 ) ^ { 2 } ( x - 9 ) ^ { 3 }$

(Multiple Choice)

4.8/5

(36)

Question 445

Solve the problem. -Imelda bought a truck for her business and depreciated it over 5 years using the straight-line method. If its value 3 years later was $\$ 6872$ , how much did she pay for it?

(Multiple Choice)

4.8/5

(32)

Question 446

Solve the problem. Round as appropriate. -The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 2?

(Multiple Choice)

4.8/5

(40)

Question 447

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - $4 , - 14$ , and $5 + 9 \mathrm { i }$

(Multiple Choice)

4.8/5

(30)

Question 448

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - $f ( x ) = - 6 x ^ { 5 }$

(Multiple Choice)

4.9/5

(45)

Question 449

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 3 x ^ { 2 } - 4 x - 4 ; d ( x ) = x ^ { 2 } + 1 \quad$ (Write answer in polynomial form)

(Multiple Choice)

4.9/5

(40)

Question 450

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { 8 x } { x - 8 } - \frac { 4 } { x } = \frac { 32 } { x ^ { 2 } - 8 x }$

(Multiple Choice)

4.8/5

(33)

Question 451

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question. -

(Multiple Choice)

4.9/5

(36)

Question 452

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 2 } - 14 x + 6 ; d ( x ) = x - 7 \quad$ (Write answer in polynomial form)

(Multiple Choice)

4.8/5

(31)

Question 453

Find the axis of the graph of the function. - $f ( x ) = 3 ( x - 2 ) ^ { 2 } + 9$

(Multiple Choice)

4.8/5

(38)

Question 454

Match the polynomial function graph to the appropriate zeros and multiplicities. -

(Multiple Choice)

4.8/5

(34)

Question 455

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { - 5 x ^ { 2 } - 8 } { x - 4 } = \frac { - 15 x } { x - 4 } + 8$

(Multiple Choice)

4.8/5

(36)

Question 456

Find the axis of the graph of the function. - $f ( x ) = ( x + 2 ) ^ { 2 } - 9$

(Multiple Choice)

4.9/5

(40)

Question 457

Find the vertex of the graph of the function. - $f ( x ) = 4 x ^ { 2 } + 40 x + 102$

(Multiple Choice)

4.8/5

(42)

Question 458

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }$

(Multiple Choice)

4.8/5

(43)

Question 459

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = 4 x ^ { 2 } - 3 x ^ { 3 } + 2 x - 5$ - $f ( x ) = 4 x ^ { 2 } - 3 x ^ { 3 } + 2 x - 5$

(Multiple Choice)

4.8/5

(37)

Question 460

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - $f ( x ) = - 2.8 x ^ { 6 }$

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 8 x - 2 ; d ( x ) = x + 4 \quad$ (Write answer in polynomial form)

Solve the problem. -Find the remainder when $x ^ { 43 } + 18$ is divided by $x - 1$ .

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 5 x - 10$ - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 5 x - 10$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 2 ( x + 9 ) ^ { 2 } ( x - 9 ) ^ { 3 }$

Solve the problem. -Imelda bought a truck for her business and depreciated it over 5 years using the straight-line method. If its value 3 years later was $\$ 6872$ , how much did she pay for it?

Solve the problem. Round as appropriate. -The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 2?

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - $4 , - 14$ , and $5 + 9 \mathrm { i }$

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - $f ( x ) = - 6 x ^ { 5 }$

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 3 x ^ { 2 } - 4 x - 4 ; d ( x ) = x ^ { 2 } + 1 \quad$ (Write answer in polynomial form)

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { 8 x } { x - 8 } - \frac { 4 } { x } = \frac { 32 } { x ^ { 2 } - 8 x }$

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question. -

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 2 } - 14 x + 6 ; d ( x ) = x - 7 \quad$ (Write answer in polynomial form)

Find the axis of the graph of the function. - $f ( x ) = 3 ( x - 2 ) ^ { 2 } + 9$

Match the polynomial function graph to the appropriate zeros and multiplicities. -

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { - 5 x ^ { 2 } - 8 } { x - 4 } = \frac { - 15 x } { x - 4 } + 8$

Find the axis of the graph of the function. - $f ( x ) = ( x + 2 ) ^ { 2 } - 9$

Find the vertex of the graph of the function. - $f ( x ) = 4 x ^ { 2 } + 40 x + 102$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }$

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = 4 x ^ { 2 } - 3 x ^ { 3 } + 2 x - 5$ - $f ( x ) = 4 x ^ { 2 } - 3 x ^ { 3 } + 2 x - 5$

Functions and Graphs

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 2: Polynomial, Power, and Rational Functions

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - f(x)=−2.8x6f ( x ) = - 2.8 x ^ { 6 }f(x)=−2.8x6

Divide f(x) by d(x), and write a summary statement in the form indicated. - f(x)=x3+5x2+8x−2;d(x)=x+4f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 8 x - 2 ; d ( x ) = x + 4 \quadf(x)=x3+5x2+8x−2;d(x)=x+4 (Write answer in polynomial form)

Solve the problem. -Find the remainder when x43+18x ^ { 43 } + 18x43+18 is divided by x−1x - 1x−1 .

Describe the end behavior of the polynomial function by finding - f(x)=x3+5x2−5x−10f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 5 x - 10f(x)=x3+5x2−5x−10

Find the zeros of the polynomial function and state the multiplicity of each. - f(x)=2(x+9)2(x−9)3f ( x ) = 2 ( x + 9 ) ^ { 2 } ( x - 9 ) ^ { 3 }f(x)=2(x+9)2(x−9)3

Solve the problem. -Imelda bought a truck for her business and depreciated it over 5 years using the straight-line method. If its value 3 years later was $6872\$ 6872$6872 , how much did she pay for it?

Solve the problem. Round as appropriate. -The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 2?

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - 4,−144 , - 144,−14 , and 5+9i5 + 9 \mathrm { i }5+9i

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - f(x)=−6x5f ( x ) = - 6 x ^ { 5 }f(x)=−6x5

Divide f(x) by d(x), and write a summary statement in the form indicated. - f(x)=x4−4x3−3x2−4x−4;d(x)=x2+1f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 3 x ^ { 2 } - 4 x - 4 ; d ( x ) = x ^ { 2 } + 1 \quadf(x)=x4−4x3−3x2−4x−4;d(x)=x2+1 (Write answer in polynomial form)

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - 8xx−8−4x=32x2−8x\frac { 8 x } { x - 8 } - \frac { 4 } { x } = \frac { 32 } { x ^ { 2 } - 8 x }x−88x​−x4​=x2−8x32​

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question. -

Divide f(x) by d(x), and write a summary statement in the form indicated. - f(x)=x2−14x+6;d(x)=x−7f ( x ) = x ^ { 2 } - 14 x + 6 ; d ( x ) = x - 7 \quadf(x)=x2−14x+6;d(x)=x−7 (Write answer in polynomial form)

Find the axis of the graph of the function. - f(x)=3(x−2)2+9f ( x ) = 3 ( x - 2 ) ^ { 2 } + 9f(x)=3(x−2)2+9

Match the polynomial function graph to the appropriate zeros and multiplicities. -

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - −5x2−8x−4=−15xx−4+8\frac { - 5 x ^ { 2 } - 8 } { x - 4 } = \frac { - 15 x } { x - 4 } + 8x−4−5x2−8​=x−4−15x​+8

Find the axis of the graph of the function. - f(x)=(x+2)2−9f ( x ) = ( x + 2 ) ^ { 2 } - 9f(x)=(x+2)2−9

Find the vertex of the graph of the function. - f(x)=4x2+40x+102f ( x ) = 4 x ^ { 2 } + 40 x + 102f(x)=4x2+40x+102

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - x2x+2=−2x4x+4+2x−3x+1\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }2x+2x​=4x+4−2x​+x+12x−3​

Describe the end behavior of the polynomial function by finding - f(x)=4x2−3x3+2x−5f ( x ) = 4 x ^ { 2 } - 3 x ^ { 3 } + 2 x - 5f(x)=4x2−3x3+2x−5

Functions and Graphs

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - $f ( x ) = - 2.8 x ^ { 6 }$

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 8 x - 2 ; d ( x ) = x + 4 \quad$ (Write answer in polynomial form)

Solve the problem. -Find the remainder when $x ^ { 43 } + 18$ is divided by $x - 1$ .

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 5 x - 10$ - $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 5 x - 10$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 2 ( x + 9 ) ^ { 2 } ( x - 9 ) ^ { 3 }$

Solve the problem. -Imelda bought a truck for her business and depreciated it over 5 years using the straight-line method. If its value 3 years later was $\$ 6872$ , how much did she pay for it?

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - $4 , - 14$ , and $5 + 9 \mathrm { i }$

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - $f ( x ) = - 6 x ^ { 5 }$

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 3 x ^ { 2 } - 4 x - 4 ; d ( x ) = x ^ { 2 } + 1 \quad$ (Write answer in polynomial form)

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { 8 x } { x - 8 } - \frac { 4 } { x } = \frac { 32 } { x ^ { 2 } - 8 x }$

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 2 } - 14 x + 6 ; d ( x ) = x - 7 \quad$ (Write answer in polynomial form)

Find the axis of the graph of the function. - $f ( x ) = 3 ( x - 2 ) ^ { 2 } + 9$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { - 5 x ^ { 2 } - 8 } { x - 4 } = \frac { - 15 x } { x - 4 } + 8$

Find the axis of the graph of the function. - $f ( x ) = ( x + 2 ) ^ { 2 } - 9$

Find the vertex of the graph of the function. - $f ( x ) = 4 x ^ { 2 } + 40 x + 102$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { x } { 2 x + 2 } = \frac { - 2 x } { 4 x + 4 } + \frac { 2 x - 3 } { x + 1 }$

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = 4 x ^ { 2 } - 3 x ^ { 3 } + 2 x - 5$ - $f ( x ) = 4 x ^ { 2 } - 3 x ^ { 3 } + 2 x - 5$