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Chapter 4: Q. 29 (page 234)

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

F(x)=x2+x-12x+2

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionF(x)=x2+x-12x+2

02

Factoring the numerator and denominator

Factoring, we get

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

03

Calculate the domain

Setting the denominator to zero, we get

x+2=0x=-2

The domain is all real numbers except-2

04

Calculate the x intercept 

Setting the numerator to zero, we get

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

Theyintercept isF(0)=-6i.e.(0,-6)

05

Calculate the vertical asymptote

The vertical asymptote is zeroes of denominator

x=-2

06

Calculate the horizontal asymptote

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

F(x)=x-1+10x+2

The oblique asymptote is y=x-1

F(x)=x2+x-12x+2=x-10=10

This is not true so it doesn't intersectF

07

Sketching the graph

The graph is

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Most popular questions from this chapter

True or False. The graph of a rational function may intersect

a horizontal asymptote.

Graph each rational function using transformations.

F(x)=2-1x+1

Find the domain of the rational function.

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f(x)=4x5+12x4-x-3

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