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Chapter 4: Q. 38 (page 234)

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

R(x)=x2+x-30x+6

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionR(x)=x2+x-30x+6

02

Factoring the numerator and denominator

Factoring, we get

R(x)=x2+x-30x+6R(x)=x2+6x-5x-30x+6R(x)=x(x+6)-5(x+6)x+6R(x)=(x-5)(x+6)(x+6)R(x)=x-5

03

Calculate the domain

Setting to zero, we get

x-5=0x=5

The domain is all real numbers except5

04

Calculate the x intercept

Thexintercept is(5,0)and theyintercept is(0,-5)

05

Calculate the vertical asymptote

There is no denominator so there is no vertical asymptote

06

Calculate the horizontal asymptote

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

y=x-5is the oblique asymptote

R(x)=x-51=x-5x-5=x-50=0

It doesn't intersectR

07

Sketching the graph

The graph is

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Most popular questions from this chapter

Use the Factor Theorem to prove that x+c is a factor of

role="math" localid="1646067091231" xn+cn if n≥1 is an odd integer

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 5000cubic inches. See the illustration.

Part (a): Express the surface areaS of the box as a function ofx.

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?

Solve the given inequality algebraically.

x4>1

In Problems63–72, find the real solutions of each equation.

2x3-11x2+10x+8=0

True or False. If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients give rise to the horizontal asymptote.
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