Exam 2: Polynomial, Power, and Rational Functions

Solve the problem. -Ariel, a marine biologist, models a population P of crabs, t days after being left to reproduce, with the function $\mathrm { P } ( \mathrm { t } ) = - 0.00009 \mathrm { t } ^ { 3 } + 0.024 \mathrm { t } ^ { 2 } + 10.5 \mathrm { t } + 1800$ Assuming that this model continues to be accurate, when will this population become extinct? (Round to the nes day.)

(Multiple Choice)

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Question 61

Find all rational zeros. - $f ( x ) = 12 x ^ { 3 } + 73 x ^ { 2 } + 5 x - 6$

(Multiple Choice)

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Question 62

Solve the problem. -If the average cost per unit $C ( x )$ (in dollars) to produce $x$ units of plywood is given by $C ( x ) = \frac { 1200 } { x + 40 }$ , what is the unit cost for 40 units?

(Multiple Choice)

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Question 63

List the x- and y-intercepts, and graph the function. - $f ( x ) = \frac { 1 } { x - 5 }$ $List the x- and y-intercepts, and graph the function. - f ( x ) = \frac { 1 } { x - 5 }$

(Multiple Choice)

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Question 64

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

(Multiple Choice)

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Question 65

Find the requested function. -Find the polynomial function with leading coefficient $- 8$ ; degree 3 ; and $5 , \frac { 1 } { 3 }$ , and $\frac { 5 } { 3 }$ as zeros.

(Multiple Choice)

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Question 66

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 20 x - 32$

(Multiple Choice)

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Question 67

Write the word or phrase that best completes each statement or answers the question. Write a sentence that expresses the relationship in the formula, using the language of variation or proportion. - $\mathrm { f } = \frac { \mathrm { m } ^ { 2 } \mathrm { v } } { \mathrm { r } } \text {, where } \mathrm { f } \text { is the centripetal force of an object of mass } \mathrm { m } \text { moving along a circle of radius } \mathrm { r } \text { at velocity } \mathrm { v }$

(Essay)

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Question 68

Find all rational zeros. - $f ( x ) = 8 x ^ { 3 } + 26 x ^ { 2 } - 23 x + 4$

(Multiple Choice)

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Question 69

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -2 (multiplicity 2) and $1 + 3 i$ (multiplicity 1 )

(Multiple Choice)

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Question 70

Write the statement as a power function equation. Use k as the constant of variation. -The area of an equilateral triangle varies directly as the square of the side s.

(Multiple Choice)

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Question 71

Use limits to describe the behavior of the rational function near the indicated asymptote. - $f ( x ) = \frac { 1 } { x ^ { 2 } - 9 }$ Describe the behavior of the function near its vertical asymptotes.

(Multiple Choice)

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Question 72

Solve the problem. -The ages and lengths of several animals of the same species are recorded in the following table: Find the linear regression model.

(Multiple Choice)

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Question 73

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = - ( x - 3 ) ( x + 1 ) ( x + 6 ) ^ { 2 }$ - $f ( x ) = - ( x - 3 ) ( x + 1 ) ( x + 6 ) ^ { 2 }$

(Multiple Choice)

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Question 74

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( 2,4 )$ , point $( 5,22 )$

(Multiple Choice)

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Question 75

Determine whether the power function is even, odd, or neither. - $f ( x ) = - 7 x ^ { 4 / 7 }$

(Multiple Choice)

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Question 76

Determine whether the power function is even, odd, or neither. - $f ( x ) = - 6 x ^ { 2 / 7 }$

(Multiple Choice)

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Question 77

Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to the nearest hundredth. - $f ( x ) = 3 x ^ { 4 } + 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x + 1$

(Multiple Choice)

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Question 78

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = x ^ { 2 } \cdot | 2 x + 5 |$

(Multiple Choice)

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Question 79

Find the remainder when f(x) is divided by (x - k) - $f ( x ) = 4 x ^ { 2 } - 4 x + 1 ; k = - 3$

(Multiple Choice)

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Question 80

Find all rational zeros. - $f ( x ) = 12 x ^ { 3 } + 73 x ^ { 2 } + 5 x - 6$

Solve the problem. -If the average cost per unit $C ( x )$ (in dollars) to produce $x$ units of plywood is given by $C ( x ) = \frac { 1200 } { x + 40 }$ , what is the unit cost for 40 units?

List the x- and y-intercepts, and graph the function. - $f ( x ) = \frac { 1 } { x - 5 }$ $List the x- and y-intercepts, and graph the function. - f ( x ) = \frac { 1 } { x - 5 }$

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

Find the requested function. -Find the polynomial function with leading coefficient $- 8$ ; degree 3 ; and $5 , \frac { 1 } { 3 }$ , and $\frac { 5 } { 3 }$ as zeros.

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 20 x - 32$

Find all rational zeros. - $f ( x ) = 8 x ^ { 3 } + 26 x ^ { 2 } - 23 x + 4$

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -2 (multiplicity 2) and $1 + 3 i$ (multiplicity 1 )

Write the statement as a power function equation. Use k as the constant of variation. -The area of an equilateral triangle varies directly as the square of the side s.

Use limits to describe the behavior of the rational function near the indicated asymptote. - $f ( x ) = \frac { 1 } { x ^ { 2 } - 9 }$ Describe the behavior of the function near its vertical asymptotes.

Solve the problem. -The ages and lengths of several animals of the same species are recorded in the following table: Find the linear regression model.

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = - ( x - 3 ) ( x + 1 ) ( x + 6 ) ^ { 2 }$ - $f ( x ) = - ( x - 3 ) ( x + 1 ) ( x + 6 ) ^ { 2 }$

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( 2,4 )$ , point $( 5,22 )$

Determine whether the power function is even, odd, or neither. - $f ( x ) = - 7 x ^ { 4 / 7 }$

Determine whether the power function is even, odd, or neither. - $f ( x ) = - 6 x ^ { 2 / 7 }$

Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to the nearest hundredth. - $f ( x ) = 3 x ^ { 4 } + 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x + 1$

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = x ^ { 2 } \cdot | 2 x + 5 |$

Find the remainder when f(x) is divided by (x - k) - $f ( x ) = 4 x ^ { 2 } - 4 x + 1 ; k = - 3$

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

Find all rational zeros. - f(x)=12x3+73x2+5x−6f ( x ) = 12 x ^ { 3 } + 73 x ^ { 2 } + 5 x - 6f(x)=12x3+73x2+5x−6

Solve the problem. -If the average cost per unit C(x)C ( x )C(x) (in dollars) to produce xxx units of plywood is given by C(x)=1200x+40C ( x ) = \frac { 1200 } { x + 40 }C(x)=x+401200​ , what is the unit cost for 40 units?

List the x- and y-intercepts, and graph the function. - f(x)=1x−5f ( x ) = \frac { 1 } { x - 5 }f(x)=x−51​

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

Find the requested function. -Find the polynomial function with leading coefficient −8- 8−8 ; degree 3 ; and 5,135 , \frac { 1 } { 3 }5,31​ , and 53\frac { 5 } { 3 }35​ as zeros.

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - f(x)=x3+6x2−20x−32f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 20 x - 32f(x)=x3+6x2−20x−32

Find all rational zeros. - f(x)=8x3+26x2−23x+4f ( x ) = 8 x ^ { 3 } + 26 x ^ { 2 } - 23 x + 4f(x)=8x3+26x2−23x+4

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -2 (multiplicity 2) and 1+3i1 + 3 i1+3i (multiplicity 1 )

Write the statement as a power function equation. Use k as the constant of variation. -The area of an equilateral triangle varies directly as the square of the side s.

Use limits to describe the behavior of the rational function near the indicated asymptote. - f(x)=1x2−9f ( x ) = \frac { 1 } { x ^ { 2 } - 9 }f(x)=x2−91​ Describe the behavior of the function near its vertical asymptotes.

Solve the problem. -The ages and lengths of several animals of the same species are recorded in the following table: Find the linear regression model.

Describe the end behavior of the polynomial function by finding - f(x)=−(x−3)(x+1)(x+6)2f ( x ) = - ( x - 3 ) ( x + 1 ) ( x + 6 ) ^ { 2 }f(x)=−(x−3)(x+1)(x+6)2

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex (2,4)( 2,4 )(2,4) , point (5,22)( 5,22 )(5,22)

Determine whether the power function is even, odd, or neither. - f(x)=−7x4/7f ( x ) = - 7 x ^ { 4 / 7 }f(x)=−7x4/7

Determine whether the power function is even, odd, or neither. - f(x)=−6x2/7f ( x ) = - 6 x ^ { 2 / 7 }f(x)=−6x2/7

Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to the nearest hundredth. - f(x)=3x4+6x3−3x2+3x+1f ( x ) = 3 x ^ { 4 } + 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x + 1f(x)=3x4+6x3−3x2+3x+1

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - f(x)=x2⋅∣2x+5∣f ( x ) = x ^ { 2 } \cdot | 2 x + 5 |f(x)=x2⋅∣2x+5∣

Find the remainder when f(x) is divided by (x - k) - f(x)=4x2−4x+1;k=−3f ( x ) = 4 x ^ { 2 } - 4 x + 1 ; k = - 3f(x)=4x2−4x+1;k=−3

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

Find all rational zeros. - $f ( x ) = 12 x ^ { 3 } + 73 x ^ { 2 } + 5 x - 6$

Solve the problem. -If the average cost per unit $C ( x )$ (in dollars) to produce $x$ units of plywood is given by $C ( x ) = \frac { 1200 } { x + 40 }$ , what is the unit cost for 40 units?

List the x- and y-intercepts, and graph the function. - $f ( x ) = \frac { 1 } { x - 5 }$ $List the x- and y-intercepts, and graph the function. - f ( x ) = \frac { 1 } { x - 5 }$

Find the requested function. -Find the polynomial function with leading coefficient $- 8$ ; degree 3 ; and $5 , \frac { 1 } { 3 }$ , and $\frac { 5 } { 3 }$ as zeros.

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 20 x - 32$

Find all rational zeros. - $f ( x ) = 8 x ^ { 3 } + 26 x ^ { 2 } - 23 x + 4$

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. -2 (multiplicity 2) and $1 + 3 i$ (multiplicity 1 )

Use limits to describe the behavior of the rational function near the indicated asymptote. - $f ( x ) = \frac { 1 } { x ^ { 2 } - 9 }$ Describe the behavior of the function near its vertical asymptotes.

Describe the end behavior of the polynomial function by finding $Describe the end behavior of the polynomial function by finding - f ( x ) = - ( x - 3 ) ( x + 1 ) ( x + 6 ) ^ { 2 }$ - $f ( x ) = - ( x - 3 ) ( x + 1 ) ( x + 6 ) ^ { 2 }$

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( 2,4 )$ , point $( 5,22 )$

Determine whether the power function is even, odd, or neither. - $f ( x ) = - 7 x ^ { 4 / 7 }$

Determine whether the power function is even, odd, or neither. - $f ( x ) = - 6 x ^ { 2 / 7 }$

Use a graphing calculator to approximate the real zeros of the function defined by f(x). Express decimal approximations to the nearest hundredth. - $f ( x ) = 3 x ^ { 4 } + 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x + 1$

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = x ^ { 2 } \cdot | 2 x + 5 |$

Find the remainder when f(x) is divided by (x - k) - $f ( x ) = 4 x ^ { 2 } - 4 x + 1 ; k = - 3$