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Chapter 4: Q. 28 (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-12x+5

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionR(x)=x2-x-12x+5

02

Factoring the numerator and denominator

Factoring, we get

R(x)=x2-x-12x+5R(x)=x2-4x+3x-12x+5R(x)=x(x-4)+3(x-4)x+5R(x)=(x+3)(x-4)(x+5)

03

Calculating the domain

On setting the denominator to zero,

x=-5

The domain is all real numbers exceptx=-5

04

Calculate the x intercept

Setting numerator to zero, we get

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

Theyintercept isR(0)=-125i.e.(0,-125)

05

Calculating the vertical asymptote

The vertical asymptote is zeroes of denominator i.e.x=-5

06

Calculating the horizontal asymptote

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

R(x)=x-6+18x+5

The oblique asymptote isy=x-6

07

Sketching the graph

The graph is

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