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Chapter 4: Q. 17 (page 234)

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

R(x)=x2x2+x-6

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given the functionR(x)=x2x2+x-6

02

Factor the numerator and denominator 

Factoring, we get

R(x)=x2x2+x-6R(x)=x2x2+3x-2x-6R(x)=x2x(x+3)-2(x+3)R(x)=x2(x-2)(x+3)

03

Calculate the domain

On setting the denominator to zero, we get

x=2,-3

So the domain is all real numbers except2,-3

04

Substitute numerator to zero to get  x intercept

Substituting, we get

x2=0x=0

There is nox,yintercept

05

Calculate the vertical asymptote

On setting the denominator to zero, we get

x=2,-3as the vertical asymptote

06

Calculation of horizontal asymptote

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

y=11y=1

07

Sketching the graph

The graph is

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