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Chapter 4: Q. 44 (page 234)

In Problems 7-44, follow Steps 1 through 7 on page 228 to analyze the graph of each function.

f(x)=2x+9x3

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given the functionf(x)=2x+9x3

02

Factoring the numerator and denominator

Factoring, we get

f(x)=2x+9x3f(x)=2x4+9x3

03

Calculate the domain

Calculating, we get

x3=0x=0

The domain is all real numbers0

04

Calculate the x intercept

Setting numerator to zero, we get

2x4+9=0x4=-92

There is nox,yintercept

05

Calculate the vertical asymptote

The zeroes of denominator is the vertical asymptote sox=0is the vertical asymptote

06

Calculating the horizontal asymptote

The degree of numerator is greater than denominator so there is an oblique asymptote

y=2xis the oblique asymptote

f(x)=2x4+9x=2x2x4+9=2x22x4-2x2=-9

It doesn't intersectf

07

Sketching the graph

The graph is

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Most popular questions from this chapter

Solve the inequality algebraically.

x3+2x2-3x>0

For a rational functionR, if the degree of the numerator is less than the degree of the denominator, then R is ________.

Graph each rational function using transformations.

R(x)=1x-1+1

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000cubic inches. See the illustration.

Part (a): Express the surface area S of the box as a function of x.

Part (b): Using a graphing utility, graph the function found in part (a).

Part (c): What is the minimum amount of cardboard that can be used to construct the box?

Part (d): What are the dimensions of the box that minimize the surface are?

Part (e): Why might UPS be interested in designing a box that minimizes the surface area?

In Problems 7-44, follow Steps 1through 7 on page 228to analyze the graph of each function.

G(x)=x3+1x2+2x
See all solutions

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