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Chapter 4: Q. 25 (page 234)

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

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

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionF(x)=x2-3x-4x+2

02

Factoring the numerator and denominator

Factoring, we get

F(x)=x2-3x-4x+2F(x)=x2-4x+x-4x+2F(x)=x(x-4)+1(x-4)x+2F(x)=(x+1)(x-4)(x+2)

03

Calculating the domain

Setting denominator to zero, we get

x+2=0x=-2

The domain is all real numbers except-2

04

Calculating the x intercept 

Setting numerator to zero, we get

(x+1)(x-4)=0x=-1,4

Theyintercept isF(0)=-2i.e.(0,-2)

05

Calculating the vertical asymptote

Setting denominator to zero, we get

x=-2

06

Calculate the horizontal asymptote

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

The oblique asymptote isy=x-5

07

Sketching the graph

The graph is

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Most popular questions from this chapter

Graph each rational function using transformations.

R(x)=1x-1+1

Find the real zeros of f. Use the real zeros to factor f.

f(x)=2x3-13x2+24x-9

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

G(x)=x3+1x2+2x

Find the domain of the rational function.

Rx=4xx-3

Find the domain of the rational function.

Hx=3x2+xx2+4
See all solutions

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