Exam 4: Polynomials and Rational Functions

The average cost for an adult funeral in Oak City has increased as shown in the table below: $\begin{array} { c | c } \text { Year } & \text { Cost (\$) } \\\hline 0 & 1600 \\5 & 2450 \\11 & 3470 \\15 & 4150 \\16 & 4320 \\18 & 4660\end{array}$ Use a linear function to estimate the cost of an adult funeral in year 20 and 30.

(Multiple Choice)

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Question 41

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 4 ) ^ { 2 } + 6$

(Multiple Choice)

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Question 42

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - \frac { 1 } { 3 } ; f ( x ) = - 3 x ^ { 4 } + 8 x ^ { 3 } + 2 x + 1$

(True/False)

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Question 43

Find the equation that the given graph represents. -

(Multiple Choice)

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Question 44

Sketch the graph of the polynomial function. -

(Multiple Choice)

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Question 45

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$ -intercepts?

(Multiple Choice)

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Question 46

Determine whether the statement is true or false. - $f(x)=\frac{10}{x^{2}}-1$ $Determine whether the statement is true or false. - f(x)=\frac{10}{x^{2}}-1$

(Multiple Choice)

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Question 47

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 4 ( x + 8 ) ^ { 2 } ( x - 8 ) ^ { 3 }$

(Multiple Choice)

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Question 48

$\text { If } x \text { varies inversely as } y ^ { 2 } \text {, and } x = 2 \text { when } y = 20 \text {, find } x \text { when } y = 5 \text {. }$

(Multiple Choice)

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Question 49

Determine whether the statement is true or false. - $f(x)=\frac{3}{x}-4$ $Determine whether the statement is true or false. - f(x)=\frac{3}{x}-4$

(Multiple Choice)

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Question 50

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18$

(Multiple Choice)

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Question 51

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $3 , i , - i$ and $P ( 2 ) = 30$

(Multiple Choice)

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Question 52

Find a polynomial of least degree with only real coefficients and having the given zeros. - $6 + 5 i$ and $6 - 5 i$

(Multiple Choice)

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Question 53

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { x + 1 } { x ^ { 2 } } \text { is an even function. }$

(True/False)

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Question 54

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-5)^{2}+1$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-5)^{2}+1 Find the domain and range.$ Find the domain and range.

(Multiple Choice)

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Question 55

Determine which of the rational functions given below has the following feature(s). -The y-intercept is (0, 4)

(Multiple Choice)

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Question 56

Translate the given formula to an English phrase using the word "varies". - $\mathrm { V } = \pi \mathrm { r } ^ { 2 } \mathrm {~h}$ h, where V is the volume of a cylinder of radius r and height h.

(Essay)

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Question 57

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; x - 4$

(True/False)

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Question 58

A rock is propelled upward from the top of a building 110 feet tall at an initial velocity of 200 feet per second. Give the function that describes the height of the rocket in terms of time t.

(Multiple Choice)

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Question 59

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } - 9 }$

(Multiple Choice)

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Question 60

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 4 ) ^ { 2 } + 6$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - \frac { 1 } { 3 } ; f ( x ) = - 3 x ^ { 4 } + 8 x ^ { 3 } + 2 x + 1$

Find the equation that the given graph represents. -

Sketch the graph of the polynomial function. -

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$ -intercepts?

Determine whether the statement is true or false. - $f(x)=\frac{10}{x^{2}}-1$ $Determine whether the statement is true or false. - f(x)=\frac{10}{x^{2}}-1$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 4 ( x + 8 ) ^ { 2 } ( x - 8 ) ^ { 3 }$

$\text { If } x \text { varies inversely as } y ^ { 2 } \text {, and } x = 2 \text { when } y = 20 \text {, find } x \text { when } y = 5 \text {. }$

Determine whether the statement is true or false. - $f(x)=\frac{3}{x}-4$ $Determine whether the statement is true or false. - f(x)=\frac{3}{x}-4$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $3 , i , - i$ and $P ( 2 ) = 30$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $6 + 5 i$ and $6 - 5 i$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { x + 1 } { x ^ { 2 } } \text { is an even function. }$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-5)^{2}+1$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-5)^{2}+1 Find the domain and range.$ Find the domain and range.

Determine which of the rational functions given below has the following feature(s). -The y-intercept is (0, 4)

Translate the given formula to an English phrase using the word "varies". - $\mathrm { V } = \pi \mathrm { r } ^ { 2 } \mathrm {~h}$ h, where V is the volume of a cylinder of radius r and height h.

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; x - 4$

A rock is propelled upward from the top of a building 110 feet tall at an initial velocity of 200 feet per second. Give the function that describes the height of the rocket in terms of time t.

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } - 9 }$

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

Find the equation of the axis of symmetry of the parabola. - f(x)=(x+4)2+6f ( x ) = ( x + 4 ) ^ { 2 } + 6f(x)=(x+4)2+6

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=−13;f(x)=−3x4+8x3+2x+1k = - \frac { 1 } { 3 } ; f ( x ) = - 3 x ^ { 4 } + 8 x ^ { 3 } + 2 x + 1k=−31​;f(x)=−3x4+8x3+2x+1

Find the equation that the given graph represents. -

Sketch the graph of the polynomial function. -

Provide an appropriate response. -For what values of a does the quadratic function f(x)=ax2−6x+3f ( x ) = a x ^ { 2 } - 6 x + 3f(x)=ax2−6x+3 have no xxx -intercepts?

Determine whether the statement is true or false. - f(x)=10x2−1f(x)=\frac{10}{x^{2}}-1f(x)=x210​−1

Find the zeros of the polynomial function and state the multiplicity of each. - f(x)=4(x+8)2(x−8)3f ( x ) = 4 ( x + 8 ) ^ { 2 } ( x - 8 ) ^ { 3 }f(x)=4(x+8)2(x−8)3

If x varies inversely as y2, and x=2 when y=20, find x when y=5. \text { If } x \text { varies inversely as } y ^ { 2 } \text {, and } x = 2 \text { when } y = 20 \text {, find } x \text { when } y = 5 \text {. } If x varies inversely as y2, and x=2 when y=20, find x when y=5.

Determine whether the statement is true or false. - f(x)=3x−4f(x)=\frac{3}{x}-4f(x)=x3​−4

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x3+7x2−16x+18f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18f(x)=x3+7x2−16x+18

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of 3,i,−i3 , i , - i3,i,−i and P(2)=30P ( 2 ) = 30P(2)=30

Find a polynomial of least degree with only real coefficients and having the given zeros. - 6+5i6 + 5 i6+5i and 6−5i6 - 5 i6−5i

Determine whether the statement is true or false. - The function f(x)=x+1x2 is an even function. \text { The function } f ( x ) = \frac { x + 1 } { x ^ { 2 } } \text { is an even function. } The function f(x)=x2x+1​ is an even function.

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=−2(x−5)2+1f(x)=-2(x-5)^{2}+1f(x)=−2(x−5)2+1 Find the domain and range.

Determine which of the rational functions given below has the following feature(s). -The y-intercept is (0, 4)

Translate the given formula to an English phrase using the word "varies". - V=πr2 h\mathrm { V } = \pi \mathrm { r } ^ { 2 } \mathrm {~h}V=πr2 h h, where V is the volume of a cylinder of radius r and height h.

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - x3−6x2+13x−20;x−4x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; x - 4x3−6x2+13x−20;x−4

A rock is propelled upward from the top of a building 110 feet tall at an initial velocity of 200 feet per second. Give the function that describes the height of the rocket in terms of time t.

Give the equations of any vertical asymptotes. - f(x)=x−1x2−9f ( x ) = \frac { x - 1 } { x ^ { 2 } - 9 }f(x)=x2−9x−1​

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

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 4 ) ^ { 2 } + 6$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - \frac { 1 } { 3 } ; f ( x ) = - 3 x ^ { 4 } + 8 x ^ { 3 } + 2 x + 1$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$ -intercepts?

Determine whether the statement is true or false. - $f(x)=\frac{10}{x^{2}}-1$ $Determine whether the statement is true or false. - f(x)=\frac{10}{x^{2}}-1$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 4 ( x + 8 ) ^ { 2 } ( x - 8 ) ^ { 3 }$

$\text { If } x \text { varies inversely as } y ^ { 2 } \text {, and } x = 2 \text { when } y = 20 \text {, find } x \text { when } y = 5 \text {. }$

Determine whether the statement is true or false. - $f(x)=\frac{3}{x}-4$ $Determine whether the statement is true or false. - f(x)=\frac{3}{x}-4$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $3 , i , - i$ and $P ( 2 ) = 30$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $6 + 5 i$ and $6 - 5 i$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { x + 1 } { x ^ { 2 } } \text { is an even function. }$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=-2(x-5)^{2}+1$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=-2(x-5)^{2}+1 Find the domain and range.$ Find the domain and range.

Translate the given formula to an English phrase using the word "varies". - $\mathrm { V } = \pi \mathrm { r } ^ { 2 } \mathrm {~h}$ h, where V is the volume of a cylinder of radius r and height h.

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $x ^ { 3 } - 6 x ^ { 2 } + 13 x - 20 ; x - 4$

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } - 9 }$