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Chapter 4: Q. 18 (page 234)

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

R(x)=x2+x-12x2-4

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given the functionR(x)=x2+x-12x2-4

02

Factor the numerator and denominator

Factoring, we get

R(x)=x2+x-12x2-4R(x)=x2+4x-3x-12(x-2)(x+2)R(x)=x(x+4)-3(x+4)(x-2)(x+2)R(x)=(x-3)(x+4)(x-2)(x+2)

03

Calculate the domain

On setting the denominator to zero, we get

x=-2,2

04

Substitute numerator equal to zero to get the x intercept

Substituting, we get

(x-3)(x+4)=0x=3,-4

The xintercept is (3,0),(-4,0)

Theyintercept isR(0)=3

05

Calculate the vertical asymptote

Substituting the denominator to zero, we get

(x-2)(x+2)=0x=-2,2is the vertical asymptote

06

Calculation of horizontal asymptote

Here the degree of numerator and denominator is same so the horizontal asymptote is

y=aby=11y=1

07

Sketching the graph

The graph is

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Most popular questions from this chapter

In Problems 13鈥�24, find the domain of each rational function.

R(x)=3(x2-x-6)4(x2-9)

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.

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