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Chapter 4: Q. 33 (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-12x2-x-6

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionR(x)=x2+x-12x2-x-6

02

Factoring numerator and denominator

Factoring, we get

R(x)=x2+x-12x2-x-6R(x)=x2+4x-3x-12x2-3x+2x-6R(x)=x(x+4)-3(x+4)x(x-3)+2(x-3)R(x)=(x-3)(x+4)(x+2)(x-3)

03

Calculating the domain

Setting denominator to zero, we get

(x+2)(x-3)=0x=-2,3

The domain is all real numbers except-2,3

04

Calculating x intercept

Setting numerator to zero, we get

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

Theyintercept isR(0)=2i.e.(0,2)

05

Calculate the vertical asymptote

The zeroes of the denominator is x=-2,3so the vertical asymptote isx=-2,3

06

Calculate the horizontal asymptote

The degree of numerator is same as denominator so the horizontal asymptote is

y=aby=11y=1

07

Sketching the graph

The graph is

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