Precalculus Enhanced with Graphing Utilities

Michael Sullivan III

Chapter 4

Polynomial and Rational Functions - all with Video Answers

Educators

Section 1

Polynomial Functions and Models

Problem 1

The intercepts of the equation $9 x^{2}+4 y=36$ are________(pp. 18-19)

AG

Ankit Gupta

Numerade Educator

Problem 2

Is the expression $4 x^{3}-3.6 x^{2}-\sqrt{2}$ a polynomial? If so, what is its degree? (pp. A22-A23)

AG

Ankit Gupta

Numerade Educator

Problem 3

To graph $y=x^{2}-4$, you would shift the graph of $y=x^{2}$_______a distance of _______units. (pp. 106-114)

Charles Carter

Numerade Educator

Problem 4

Use a graphing utility to approximate (rounded to two decimal places) the local maximum value and local minimum value of $f(x)=x^{3}-2 x^{2}-4 x+5$, for $-3 \leq x \leq 3$. (pp. $87-88$ )

Colin O'Haire

Numerade Educator

Problem 5

True or False The $x$-intercepts of the graph of a function $y=f(x)$ are the real solutions of the equation $f(x)=0$. (pp. 73-75)

AG

Ankit Gupta

Numerade Educator

Problem 6

If $g(5)=0$, what point is on the graph of $g$ ? What is the corresponding $x$-intercept of the graph of $g$ ? (pp. 73-75)

Charles Carter

Numerade Educator

Problem 7

The graph of every polynomial function is both_______ and_______

AG

Ankit Gupta

Numerade Educator

Problem 8

If $r$ is a real zero of even multiplicity of a polynomial function $f$, then the graph of $f$________ (crosses/touches) the $x$-axis at $r$.

AG

Ankit Gupta

Numerade Educator

Problem 9

The graphs of power functions of the form $f(x)=x^{n}$, where $n$ is an even integer, always contain the points_______ _______
, and_______

Maninder Singh

Numerade Educator

Problem 10

If $r$ is a solution to the equation $f(x)=0$, name three additional statements that can be made about $f$ and $r$, assuming $f$ is a polynomial function.

Maninder Singh

Numerade Educator

Problem 11

The points at which a graph changes direction (from increasing to decreasing or decreasing to increasing) are called_______

Maninder Singh

Numerade Educator

Problem 12

For the function $f(x)=3 x^{4}, \lim _{x \rightarrow-\infty} f(x)=$ $\lim _{x \rightarrow \infty} f(x)=$

Bobby Barnes

University of North Texas

Problem 13

If $f(x)=-2 x^{5}+x^{3}-5 x^{2}+7$, then $\lim _{x \rightarrow-\infty} f(x)=$_____ and $\lim _{x \rightarrow \infty} f(x)=$_____

Maninder Singh

Numerade Educator

Problem 14

Explain what the notation $\lim _{x \rightarrow \infty} f(x)=-\infty$ means.

Maninder Singh

Numerade Educator

Problem 15

The _____of a zero is the number of times its corresponding factor occurs
(a) degree
(b) multiplicity
(c) turning point
(d) limit

JK

Jeffrey Kearin

Numerade Educator

Problem 16

The graph of $y=5 x^{6}-3 x^{4}+2 x-9$ has at most how many turning points?
(a) $-9$
(b) 14
(c) 6
(d) 5

AG

Ankit Gupta

Numerade Educator

Problem 17

In Problems 17-28, determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term.
$f(x)=4 x+x^{3}$

Donna Densmore

Numerade Educator

Problem 18

$f(x)=5 x^{2}+4 x^{4}$

Todd Vawdrey

Numerade Educator

Problem 19

$g(x)=\frac{1-x^{2}}{2}$

Carson Merrill

Numerade Educator

Problem 20

$h(x)=3-\frac{1}{2} x$

Yujie Wang

College of San Mateo

Problem 21

$f(x)=1-\frac{1}{x}$

Taylor Shimono

Numerade Educator

Problem 22

$f(x)=x(x-1)$

Taylor Shimono

Numerade Educator

Problem 23

$g(x)=x^{3 / 2}-x^{2}+2$

AG

Ankit Gupta

Numerade Educator

Problem 24

$h(x)=\sqrt{x}(\sqrt{x}-1)$

AG

Ankit Gupta

Numerade Educator

Problem 25

$F(x)=5 x^{4}-\pi x^{3}+\frac{1}{2}$

Mirza Aslam Beig

Mirza Aslam Beig

Numerade Educator

Problem 26

$F(x)=\frac{x^{2}-5}{x^{3}}$

Alan Mullenix

Numerade Educator

Problem 27

$G(x)=2(x-1)^{2}\left(x^{2}+1\right)$

Carson Merrill

Numerade Educator

Problem 28

$G(x)=-3 x^{2}(x+2)^{3}$

James Kiss

Numerade Educator

Problem 29

In Problems 29-42, use transformations of the graph of $y=x^{4}$ or $y=x^{5}$ to graph each function.
$f(x)=(x+1)^{4}$

Leslie Deeb

Numerade Educator

Problem 30

$f(x)=(x-2)^{5}$

Taylor Shimono

Numerade Educator

Problem 31

$f(x)=x^{5}-3$

Taylor Shimono

Numerade Educator

Problem 32

$f(x)=x^{4}+2$

Bobby Barnes

University of North Texas

Problem 33

$f(x)=\frac{1}{2} x^{4}$

Alan Mullenix

Numerade Educator

Problem 34

$f(x)=3 x^{5}$

Taylor Shimono

Numerade Educator

Problem 35

$f(x)=-x^{5}$

Taylor Shimono

Numerade Educator

Problem 36

$f(x)=-x^{4}$

Bobby Barnes

University of North Texas

Problem 37

$f(x)=(x-1)^{5}+2$

Taylor Shimono

Numerade Educator

Problem 38

$f(x)=(x+2)^{4}-3$

Alan Mullenix

Numerade Educator

Problem 39

$f(x)=2(x+1)^{4}+1$

Lucas Finney

Numerade Educator

Problem 40

$f(x)=\frac{1}{2}(x-1)^{5}-2$

Taylor Shimono

Numerade Educator

Problem 41

$f(x)=4-(x-2)^{5}$

Todd Vawdrey

Numerade Educator

Problem 42

$f(x)=3-(x+2)^{4}$

Alan Mullenix

Numerade Educator

Problem 43

In Problems 43-50, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.
Zeros: $-1$. 1. 3: degree 3

Charles Carter

Numerade Educator

Problem 44

Zeros: $-2.2 .3$ : degree 3

AI

Alisa Ialacci

Numerade Educator

Problem 45

Zeros: $-3,0,4$; degree 3

AI

Alisa Ialacci

Numerade Educator

Problem 46

Zeros: $-4,0,2$; degree 3

AI

Alisa Ialacci

Numerade Educator

Problem 47

Zeros: $-4,-1,2,3$; degree 4

AI

Alisa Ialacci

Numerade Educator

Problem 48

Zeros: $-3,-1,2,5$; degree 4

AI

Alisa Ialacci

Numerade Educator

Problem 49

Zeros: $-1$, multiplicity $1 ; 3$, multiplicity 2 ; degree 3

James Kiss

Numerade Educator

Problem 50

Zeros: $-2$, multiplicity $2 ; 4$, multiplicity 1 ; degree 3

James Kiss

Numerade Educator

Problem 51

In Problems 51-56, find the polynomial function with the given zeros whose graph passes through the given point.
Zeros: $-3,1,4$

Leslie Deeb

Numerade Educator

Problem 52

Zeros: $-2,0,2$
Point: $(-4,16)$

AG

Ankit Gupta

Numerade Educator

Problem 53

Zeros: $-1,0,2,4$
Point: $\left(\frac{1}{2}, 63\right)$

AG

Ankit Gupta

Numerade Educator

Problem 54

Zeros: $-5,-1,2,6$
Point: $\left(\frac{5}{2}, 15\right)$

AG

Ankit Gupta

Numerade Educator

Problem 55

Zeros: - 1 (multiplicity 2 ),
1 (multiplicity 2)
Point: $(-2,45)$

AG

Ankit Gupta

Numerade Educator

Problem 56

Zeros: 0 (multiplicity 1), $-1,3$ (multiplicity 2)
Point: $(1,-48)$

AG

Ankit Gupta

Numerade Educator

Problem 57

In Problems 57-68, for each polynomial function:
(a) List each real zero and its multiplicity.
(b) Determine whether the graph crosses or touches the $x$-axis at each $x$-intercept.
(c) Determine the maximum number of turning points on the graph.
(d) Determine the end behavior; that is, find the power function that the graph of $f$ resembles for large values of $|x|$.
$f(x)=3(x-7)(x+3)^{2}$

Nicole Hoffman

Numerade Educator

Problem 58

$f(x)=4(x+4)(x+3)^{3}$

Bobby Barnes

University of North Texas

Problem 59

$f(x)=4\left(x^{2}+1\right)(x-2)^{3}$

Bobby Barnes

University of North Texas

Problem 60

$f(x)=2(x-3)\left(x^{2}+4\right)^{3}$

Alan Mullenix

Numerade Educator

Problem 61

$f(x)=-2\left(x+\frac{1}{2}\right)^{2}(x+4)^{3}$

Alan Mullenix

Numerade Educator

Problem 62

$f(x)=\left(x-\frac{1}{3}\right)^{2}(x-1)^{3}$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 63

$f(x)=(x-5)^{3}(x+4)^{2}$

Todd Vawdrey

Numerade Educator

Problem 64

$f(x)=(x+\sqrt{3})^{2}(x-2)^{4}$

Kumar Vaibhav

Numerade Educator

Problem 65

$f(x)=3\left(x^{2}+8\right)\left(x^{2}+9\right)^{2}$

Alan Mullenix

Numerade Educator

Problem 66

$f(x)=-2\left(x^{2}+3\right)^{3}$

Alan Mullenix

Numerade Educator

Problem 67

$f(x)=-2 x^{2}\left(x^{2}-2\right)$

Lucas Finney

Numerade Educator

Problem 68

$f(x)=4 x\left(x^{2}-3\right)$

Alan Mullenix

Numerade Educator

Problem 69

In Problems 69-72, identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that could not, say why not.

Jill Tolbert

Numerade Educator

Problem 70

Identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that could not, say why not.

Jill Tolbert

Numerade Educator

Problem 71

Identify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that could not, say why not.

Jill Tolbert

Numerade Educator

Problem 72

Dentify which of the graphs could be the graph of a polynomial function. For those that could, list the real zeros and state the least degree the polynomial can have. For those that could not, say why not.

Jill Tolbert

Numerade Educator

Problem 73

Construct a polynomial function that might have the given graph. (More than one answer may be possible.)

Jill Tolbert

Numerade Educator

Problem 74

Construct a polynomial function that might have the given graph. (More than one answer may be possible.)

Jill Tolbert

Numerade Educator

Problem 75

Construct a polynomial function that might have the given graph. (More than one answer may be possible.)

Jill Tolbert

Numerade Educator

Problem 76

Construct a polynomial function that might have the given graph. (More than one answer may be possible.)

Jill Tolbert

Numerade Educator

Problem 77

Write a polynomial function whose graph is shown (use the smallest degree possible).

Jill Tolbert

Numerade Educator

Problem 78

Write a polynomial function whose graph is shown (use the smallest degree possible).

Jill Tolbert

Numerade Educator

Problem 79

Write a polynomial function whose graph is shown (use the smallest degree possible).

Jill Tolbert

Numerade Educator

Problem 80

Write a polynomial function whose graph is shown (use the smallest degree possible).

Jill Tolbert

Numerade Educator

Problem 81

In Problems 81-98, analyze each polynomial function by following Steps 1 through 8 on page $193 .$
$f(x)=x^{2}(x-3)$

Charles Carter

Numerade Educator

Problem 82

$f(x)=x(x+2)^{2}$

Taylor Shimono

Numerade Educator

Problem 83

$f(x)=(x+4)^{2}(1-x)$

Alan Mullenix

Numerade Educator

Problem 84

$f(x)=(x-1)(x+3)^{2}$

Alan Mullenix

Numerade Educator

Problem 85

$f(x)=-2(x+2)(x-2)^{3}$

Alan Mullenix

Numerade Educator

Problem 86

$f(x)=-\frac{1}{2}(x+4)(x-1)^{3}$

Alan Mullenix

Numerade Educator

Problem 87

$f(x)=(x+1)(x-2)(x+4)$

Ashwin Narayan

Numerade Educator

Problem 88

$f(x)=(x-1)(x+4)(x-3)$

Jack Chen

Numerade Educator

Problem 89

$f(x)=x^{2}(x-2)(x+2)$

Taylor Shimono

Numerade Educator

Problem 90

$f(x)=x^{2}(x-3)(x+4)$

Bobby Barnes

University of North Texas

Problem 91

$f(x)=(x+1)^{2}(x-2)^{2}$

Lucas Finney

Numerade Educator

Problem 92

$f(x)=(x-4)^{2}(x+2)^{2}$

Alan Mullenix

Numerade Educator

Problem 93

$f(x)=x^{2}(x+3)(x+1)$

Taylor Shimono

Numerade Educator

Problem 94

$f(x)=x^{2}(x-3)(x-1)$

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 95

$f(x)=5 x\left(x^{2}-4\right)(x+3)$

Jessica Kluck

Numerade Educator

Problem 96

$f(x)=(x-2)^{2}(x+2)(x+4)$

Bobby Barnes

University of North Texas

Problem 97

$f(x)=x^{2}(x-2)\left(x^{2}+3\right)$

Alan Mullenix

Numerade Educator

Problem 98

$f(x)=x^{2}\left(x^{2}+1\right)(x+4)$

Bobby Barnes

University of North Texas

Problem 99

In Problems 99-106, analyze each polynomial function $f$ by following Steps 1 through 8 on page $195
.$ . $f(x)=x^{3}+0.2 x^{2}-1.5876 x-0.31752$

James Kiss

Numerade Educator

Problem 100

$f(x)=x^{3}-0.8 x^{2}-4.6656 x+3.73248$

SL

Steven La

SUNY at Binghamton

Problem 101

$f(x)=x^{3}+2.56 x^{2}-3.31 x+0.89$

SL

Steven La

SUNY at Binghamton

Problem 102

$f(x)=x^{3}-2.91 x^{2}-7.668 x-3.8151$

SL

Steven La

SUNY at Binghamton

Problem 103

. $f(x)=x^{4}-2.5 x^{2}+0.5625$

Todd Vawdrey

Numerade Educator

Problem 104

$f(x)=x^{4}-18.5 x^{2}+50.2619$

Alan Mullenix

Numerade Educator

Problem 105

$f(x)=2 x^{4}-\pi x^{3}+\sqrt{5} x-4$

Todd Vawdrey

Numerade Educator

Problem 106

$f(x)=-1.2 x^{4}+0.5 x^{2}-\sqrt{3} x+2$

Bobby Barnes

University of North Texas

Problem 107

In Problems 107-114, analyze each polynomial function by following Steps 1 through 8 on page $193 .$
[Hint: You will need to first factor the polynomial].
$f(x)=4 x-x^{3}$

AG

Ankit Gupta

Numerade Educator

Problem 108

$f(x)=x-x^{3}$

Clarissa Noh

Numerade Educator

Problem 109

$f(x)=x^{3}+x^{2}-12 x$

Alan Mullenix

Numerade Educator

Problem 110

$f(x)=x^{3}+2 x^{2}-8 x$

Nick Johnson

Numerade Educator

Problem 111

$f(x)=2 x^{4}+12 x^{3}-8 x^{2}-48 x$

Alan Mullenix

Numerade Educator

Problem 112

$f(x)=4 x^{3}+10 x^{2}-4 x-10$

Jessica Kluck

Numerade Educator

Problem 113

$f(x)=-x^{5}-x^{4}+x^{3}+x^{2}$

Todd Vawdrey

Numerade Educator

Problem 114

$f(x)=-x^{5}+5 x^{4}+4 x^{3}-20 x^{2}$

Todd Vawdrey

Numerade Educator

Problem 115

In Problems 115-118, construct a polynomial function $f$ with the given characteristics.
Zeros: $-3,1,4$; degree $3 ; y$-intercept: 36

AG

Ankit Gupta

Numerade Educator

Problem 116

Zeros: $-4,-1,2$; degree $3 ; y$-intercept: 16

Kian Manafi

Numerade Educator

Problem 117

Zeros: $-5$ (multiplicity 2 ); 2 (multiplicity 1 ); 4 (multiplicity 1 );

Manisha Sarker

Numerade Educator

Problem 118

Zeros: $-4$ (multiplicity 1 ); 0 (multiplicity 3 ); 2 (multiplicity 1 ); degree 4 ; contains the point $(3,128)$
degree 5 ; contains the point $(-2,64)$

AG

Ankit Gupta

Numerade Educator

Problem 119

$$
G(x)=(x+3)^{2}(x-2)
$$
(a) Identify the $x$-intercepts of the graph of $G$.
(b) What are the $x$-intercepts of the graph of $y=G(x+3) ?$

AG

Ankit Gupta

Numerade Educator

Problem 120

$$
h(x)=(x+2)(x-4)^{3}
$$
(a) Identify the $x$-intercepts of the graph of $h$.
(b) What are the $x$-intercepts of the graph of $y=h(x-2) ?$

AG

Ankit Gupta

Numerade Educator

Problem 121

Hurricanes In 2012 , Hurricane Sandy struck the East Coast of the United States, killing 147 people and causing an estimated $\$ 75$ billion in damage. With a gale diameter of about 1000 miles, it was the largest ever to form over the Atlantic Basin. The accompanying data represent the number of major hurricane strikes in the Atlantic Basin (category 3,4 , or 5 ) each decade from 1921 to 2010 . (a) Draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables
(b) Use a graphing utility to find the cubic function of best fit that models the relation between decade and number of major hurricanes.
(c) Use the model found in part (b) to predict the number of major hurricanes that struck the Atlantic Basin between 1961 and $1970 .$
(d) With a graphing utility, draw a scatter diagram of the data and then graph the cubic function of best fit on the scatter diagram.
(e) Concern has risen about the increase in the number and intensity of hurricanes, but some scientists believe this is just a natural fluctuation that could last another decade or two. Use your model to predict the number of major hurricanes that will strike the Atlantic Basin between 2011 and 2020 . Is your result reasonable? How does this result suggest using end behavior of models to make long-term predictions is dangerous?

James Kiss

Numerade Educator

Problem 122

Poverty Rates The following data represent the percentage of people in the United States living below the poverty level. (a) With a graphing utility, draw a scatter diagram of the data. Comment on the type of relation that appears to exist between the variables.
(b) Decide on a function of best fit to these data (linear, quadratic, or cubic), and use this function to predict the percentage of people in the United States who were living below the poverty level in $2013(t=24)$. Compare your prediction to the actual value of $14.5$.
(c) Draw the function of best fit on the scatter diagram drawn in part (a).

James Kiss

Numerade Educator

Problem 123

Temperature The following data represent the temperature $T$ ('Fahrenheit) in Kansas City, Missouri, $x$ hours after midnight on March $15,2015 .$ (a) Draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables.
(b) Find the average rate of change in temperature from $9_{\mathrm{AM}}$ to 12 noon.
(c) What is the average rate of change in temperature from $3 \mathrm{PM}$ to $6 \mathrm{PM}$ ?
(d) Decide on a function of best fit to these data (linear, quadratic, or cubic) and use this function to predict the temperature at $5 \mathrm{PM}$.
(e) With a graphing utility, draw a scatter diagram of the data and then graph the function of best fit on the scatter diagram.
(f) Interpret the $y$-intercept.

Charles Carter

Numerade Educator

Problem 124

Future Value of Money Suppose that you make deposits of $\$ 500$ at the beginning of every year into an Individual Retirement Account (IRA) earning interest $r$ (expressed as a decimal). At the beginning of the first year, the value of the account will be $\$ 500$; at the beginning of the second year, the value of the account, will be
$\underbrace{\$ 500+\$ 500 r}_{\text {Value of lst deposit }}+\underbrace{\$ 500}_{\text {Value of } 2 \text { nd deposit }}=\$ 500(1+r)+\$ 500=500 r+1000$
(a) Verify that the value of the account at the beginning of the third year is $T(r)=500 r^{2}+1500 r+1500$.
(b) The account value at the beginning of the fourth year is $F(r)=500 r^{3}+2000 r^{2}+3000 r+2000$. If the annual rate of interest is $5 \%=0.05$, what will be the value of the account at the beginning of the fourth year?

Colin O'Haire

Numerade Educator

Problem 125

A Geometric Series In calculus, you will learn that certain functions can be approximated by polynomial functions. We will explore one such function now.
(a) Using a graphing utility, create a table of values with $Y_{1}=f(x)=\frac{1}{1-x}$ and $Y_{2}=g_{2}(x)=1+x+x^{2}+x^{3}$ for $-1<x<1$ with $\Delta \mathrm{Tbl}=0.1$.
(b) Using a graphing utility, create a table of values with
$$
\begin{aligned}
&Y_{1}=f(x)=\frac{1}{1-x} \text { and } \\
&Y_{2}=g_{3}(x)=1+x+x^{2}+x^{3}+x^{4} \\
&\text { for }-1<x<1 \text { with } \Delta \mathrm{Tbl}=0.1 .
\end{aligned}
$$
(c) Using a graphing utility, create a table of values with
$$
\begin{aligned}
&Y_{1}=f(x)=\frac{1}{1-x} \text { and } \\
&Y_{2}=g_{4}(x)=1+x+x^{2}+x^{3}+x^{4}+x^{5} \\
&\text { for }-1<x<1 \text { with } \Delta \mathrm{Tbl}=0.1 .
\end{aligned}
$$
(d) What do you notice about the values of the function as more terms are added to the polynomial? Are there some values of $x$ for which the approximations are better?

Charles Carter

Numerade Educator

Problem 126

If $f(x)=x^{3}$, graph $f(2 x)$.

Vicki Stebbins

Numerade Educator

Problem 127

Write a few paragraphs that provide a general strategy for graphing a polynomial function. Be sure to mention the following: degree, intercepts, end behavior, and turning points.

Charles Carter

Numerade Educator

Problem 128

Make up a polynomial that has the following characteristics: crosses the $x$-axis at $-1$ and 4 , touches the $x$-axis at 0 and 2 , and is above the $x$-axis between 0 and 2 . Give your polynomial to a fellow classmate and ask for a written critique.

Charles Carter

Numerade Educator

Problem 129

Make up two polynomials, not of the same degree, with the following characteristics: crosses the $x$-axis at $-2$, touches the $x$-axis at 1 , and is above the $x$-axis between $-2$ and 1 . Give your polynomials to a fellow classmate and ask for a written critique.

Charles Carter

Numerade Educator

Problem 130

The graph of a polynomial function is always smooth and continuous. Name a function studied earlier that is smooth but not continuous. Name one that is continuous but not smooth.

Charles Carter

Numerade Educator

Problem 131

Which of the following statements are true regarding the graph of the cubic polynomial $f(x)=x^{3}+b x^{2}+c x+d$ ? (Give reasons for your conclusions.)
(a) It intersects the $y$-axis in one and only one point.
(b) It intersects the $x$-axis in at most three points.
(c) It intersects the $x$-axis at least once.
(d) For $|x|$ very large, it behaves like the graph of $y=x^{3}$.
(e) It is symmetric with respect to the origin.
(f) It passes through the origin.

Charles Carter

Numerade Educator

Problem 132

The illustration shows the graph of a polynomial function.
(a) Is the degree of the polynomial even or odd?
(b) Is the leading coefficient positive or negative?
(c) Is the function even, odd, or neither?
(d) Why is $x^{2}$ necessarily a factor of the polynomial?
(e) What is the minimum degree of the polynomial?
(f) Formulate five different polynomials whose graphs could look like the one shown. Compare yours to those of other students. What similarities do you see? What differences?

Charles Carter

Numerade Educator

Problem 133

Design a polynomial function with the following characteristics: degree 6; four distinct real zeros, one of multiplicity $3 ; y$-intercept 3 ; behaves like $y=-5 x^{6}$ for large values of $|x|$. Is this polynomial unique? Compare your polynomial with those of other students. What terms will be the same as everyone else's? Add some more characteristics, such as symmetry or naming the real zeros. How does this modify the polynomial?

Charles Carter

Numerade Educator

Problem 134

Can the graph of a polynomial function have no $y$-intercept? Can it have no $x$-intercepts? Explain.

Charles Carter

Numerade Educator

Problem 135

Problems 135-138 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
Find the equation of the line that contains the point $(2,-3)$ and is perpendicular to the line $5 x-2 y=6$.

Sheryl Ezze

Numerade Educator

Problem 136

Find the domain of the function $h(x)=\frac{x-3}{x+5}$.

Amy Jiang

Numerade Educator

Problem 137

Find the $x$-intercepts of the graph of $f(x)=4 x^{2}+8 x-3$.

Suman Saurav Thakur

Suman Saurav Thakur

Numerade Educator

Problem 138

Solve the inequality $x^{2}<21-4 x$.

Mirza Aslam Beig

Mirza Aslam Beig

Numerade Educator