Exam 2: Polynomial, Power, and Rational Functions

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = \frac { x - 2 } { ( x - 4 ) \sqrt { x + 6 } }$

(Multiple Choice)

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Question 181

Determine if the function is a power function. If it is, then state the power and constant of variation. - $f ( x ) = - \frac { 3 } { 4 } x ^ { 5 }$

(Multiple Choice)

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Question 182

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - $f ( x ) = - 1 - 5 x - 18 x ^ { 2 } - 9 x ^ { 3 } - 12 x ^ { 4 }$

(Multiple Choice)

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Question 183

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { x + 2 } { 7 } - \frac { x - 4 } { 3 } = 2$

(Multiple Choice)

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Question 184

Provide an appropriate response. -Let $\mathrm { f }$ be a polynomial function with real coefficients. If $- 5,8 , - 7 + 4 i$ , and $6 - 5 i$ are zeros of $\mathrm { f }$ , what is the smallest possible degree that $\mathrm { f }$ can have?

(Multiple Choice)

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Question 185

State the domain of the rational function. - $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 16 }$

(Multiple Choice)

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Question 186

Graph the function. - $P(x)=-2 x(x+2)^{2}$ $Graph the function. - P(x)=-2 x(x+2)^{2}$

(Multiple Choice)

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Question 187

Find all rational zeros. - $f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } - x + 2$

(Multiple Choice)

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Question 188

Match the graph of the rational function with its equation. -

(Multiple Choice)

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Question 189

State the domain of the rational function. - $f ( x ) = \frac { x - 2 } { x ^ { 2 } + 8 x }$

(Multiple Choice)

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Question 190

List the x- and y-intercepts, and graph the function. - $f(x)=\frac{-2 x-3}{x+2}$ $List the x- and y-intercepts, and graph the function. - f(x)=\frac{-2 x-3}{x+2}$

(Multiple Choice)

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Question 191

Match the equation to the correct graph. - $y = 2 ( x + 1 ) ^ { 2 } - 2$

(Multiple Choice)

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Question 192

Find the requested function. -Find the polynomial function with leading coefficient 4 ; degree 4 ; and $- 4 , - 1,0$ , and $\frac { 3 } { 4 }$ as zeros.

(Multiple Choice)

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Question 193

Provide an appropriate response. -Determine the number of real and imaginary solutions of the equation $x ^ { 6 } = 1$ .

(Multiple Choice)

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Question 194

Describe the strength and direction of the linear correlation. -The ages and lengths of several animals of the same species are recorded in the following table:

(Multiple Choice)

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Question 195

Find the zeros of the function. - $f ( x ) = 9 x ^ { 2 } + 6 x - 8$

(Multiple Choice)

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Question 196

Find a cubic function with the given zeros. - $- 2,1 + \sqrt { 5 } , 1 - \sqrt { 5 }$

(Multiple Choice)

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Question 197

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 26 x ^ { 2 } - 18 x - 315$

(Multiple Choice)

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Question 198

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -4 and $3 + 6 i$

(Multiple Choice)

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Question 199

Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and leading coefficient. - $f ( x ) = - 8$

(Multiple Choice)

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Question 200

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = \frac { x - 2 } { ( x - 4 ) \sqrt { x + 6 } }$

Determine if the function is a power function. If it is, then state the power and constant of variation. - $f ( x ) = - \frac { 3 } { 4 } x ^ { 5 }$

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - $f ( x ) = - 1 - 5 x - 18 x ^ { 2 } - 9 x ^ { 3 } - 12 x ^ { 4 }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { x + 2 } { 7 } - \frac { x - 4 } { 3 } = 2$

Provide an appropriate response. -Let $\mathrm { f }$ be a polynomial function with real coefficients. If $- 5,8 , - 7 + 4 i$ , and $6 - 5 i$ are zeros of $\mathrm { f }$ , what is the smallest possible degree that $\mathrm { f }$ can have?

State the domain of the rational function. - $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 16 }$

Graph the function. - $P(x)=-2 x(x+2)^{2}$ $Graph the function. - P(x)=-2 x(x+2)^{2}$

Find all rational zeros. - $f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } - x + 2$

Match the graph of the rational function with its equation. -

State the domain of the rational function. - $f ( x ) = \frac { x - 2 } { x ^ { 2 } + 8 x }$

List the x- and y-intercepts, and graph the function. - $f(x)=\frac{-2 x-3}{x+2}$ $List the x- and y-intercepts, and graph the function. - f(x)=\frac{-2 x-3}{x+2}$

Match the equation to the correct graph. - $y = 2 ( x + 1 ) ^ { 2 } - 2$

Find the requested function. -Find the polynomial function with leading coefficient 4 ; degree 4 ; and $- 4 , - 1,0$ , and $\frac { 3 } { 4 }$ as zeros.

Provide an appropriate response. -Determine the number of real and imaginary solutions of the equation $x ^ { 6 } = 1$ .

Describe the strength and direction of the linear correlation. -The ages and lengths of several animals of the same species are recorded in the following table:

Find the zeros of the function. - $f ( x ) = 9 x ^ { 2 } + 6 x - 8$

Find a cubic function with the given zeros. - $- 2,1 + \sqrt { 5 } , 1 - \sqrt { 5 }$

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 26 x ^ { 2 } - 18 x - 315$

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -4 and $3 + 6 i$

Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and leading coefficient. - $f ( x ) = - 8$

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

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - f(x)=x−2(x−4)x+6f ( x ) = \frac { x - 2 } { ( x - 4 ) \sqrt { x + 6 } }f(x)=(x−4)x+6​x−2​

Determine if the function is a power function. If it is, then state the power and constant of variation. - f(x)=−34x5f ( x ) = - \frac { 3 } { 4 } x ^ { 5 }f(x)=−43​x5

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - f(x)=−1−5x−18x2−9x3−12x4f ( x ) = - 1 - 5 x - 18 x ^ { 2 } - 9 x ^ { 3 } - 12 x ^ { 4 }f(x)=−1−5x−18x2−9x3−12x4

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - x+27−x−43=2\frac { x + 2 } { 7 } - \frac { x - 4 } { 3 } = 27x+2​−3x−4​=2

Provide an appropriate response. -Let f\mathrm { f }f be a polynomial function with real coefficients. If −5,8,−7+4i- 5,8 , - 7 + 4 i−5,8,−7+4i , and 6−5i6 - 5 i6−5i are zeros of f\mathrm { f }f , what is the smallest possible degree that f\mathrm { f }f can have?

State the domain of the rational function. - f(x)=x−7x2−16f ( x ) = \frac { x - 7 } { x ^ { 2 } - 16 }f(x)=x2−16x−7​

Graph the function. - P(x)=−2x(x+2)2P(x)=-2 x(x+2)^{2}P(x)=−2x(x+2)2

Find all rational zeros. - f(x)=4x3−8x2−x+2f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } - x + 2f(x)=4x3−8x2−x+2

Match the graph of the rational function with its equation. -

State the domain of the rational function. - f(x)=x−2x2+8xf ( x ) = \frac { x - 2 } { x ^ { 2 } + 8 x }f(x)=x2+8xx−2​

List the x- and y-intercepts, and graph the function. - f(x)=−2x−3x+2f(x)=\frac{-2 x-3}{x+2}f(x)=x+2−2x−3​

Match the equation to the correct graph. - y=2(x+1)2−2y = 2 ( x + 1 ) ^ { 2 } - 2y=2(x+1)2−2

Find the requested function. -Find the polynomial function with leading coefficient 4 ; degree 4 ; and −4,−1,0- 4 , - 1,0−4,−1,0 , and 34\frac { 3 } { 4 }43​ as zeros.

Provide an appropriate response. -Determine the number of real and imaginary solutions of the equation x6=1x ^ { 6 } = 1x6=1 .

Describe the strength and direction of the linear correlation. -The ages and lengths of several animals of the same species are recorded in the following table:

Find the zeros of the function. - f(x)=9x2+6x−8f ( x ) = 9 x ^ { 2 } + 6 x - 8f(x)=9x2+6x−8

Find a cubic function with the given zeros. - −2,1+5,1−5- 2,1 + \sqrt { 5 } , 1 - \sqrt { 5 }−2,1+5​,1−5​

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - f(x)=x4−2x3−26x2−18x−315f ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 26 x ^ { 2 } - 18 x - 315f(x)=x4−2x3−26x2−18x−315

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -4 and 3+6i3 + 6 i3+6i

Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and leading coefficient. - f(x)=−8f ( x ) = - 8f(x)=−8

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

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = \frac { x - 2 } { ( x - 4 ) \sqrt { x + 6 } }$

Determine if the function is a power function. If it is, then state the power and constant of variation. - $f ( x ) = - \frac { 3 } { 4 } x ^ { 5 }$

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - $f ( x ) = - 1 - 5 x - 18 x ^ { 2 } - 9 x ^ { 3 } - 12 x ^ { 4 }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { x + 2 } { 7 } - \frac { x - 4 } { 3 } = 2$

Provide an appropriate response. -Let $\mathrm { f }$ be a polynomial function with real coefficients. If $- 5,8 , - 7 + 4 i$ , and $6 - 5 i$ are zeros of $\mathrm { f }$ , what is the smallest possible degree that $\mathrm { f }$ can have?

State the domain of the rational function. - $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 16 }$

Graph the function. - $P(x)=-2 x(x+2)^{2}$ $Graph the function. - P(x)=-2 x(x+2)^{2}$

Find all rational zeros. - $f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } - x + 2$

State the domain of the rational function. - $f ( x ) = \frac { x - 2 } { x ^ { 2 } + 8 x }$

List the x- and y-intercepts, and graph the function. - $f(x)=\frac{-2 x-3}{x+2}$ $List the x- and y-intercepts, and graph the function. - f(x)=\frac{-2 x-3}{x+2}$

Match the equation to the correct graph. - $y = 2 ( x + 1 ) ^ { 2 } - 2$

Find the requested function. -Find the polynomial function with leading coefficient 4 ; degree 4 ; and $- 4 , - 1,0$ , and $\frac { 3 } { 4 }$ as zeros.

Provide an appropriate response. -Determine the number of real and imaginary solutions of the equation $x ^ { 6 } = 1$ .

Find the zeros of the function. - $f ( x ) = 9 x ^ { 2 } + 6 x - 8$

Find a cubic function with the given zeros. - $- 2,1 + \sqrt { 5 } , 1 - \sqrt { 5 }$

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 26 x ^ { 2 } - 18 x - 315$

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -4 and $3 + 6 i$

Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and leading coefficient. - $f ( x ) = - 8$