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Chapter 4: Q. 21 (page 234)

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

R(x)=3(x-1)x2-4

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionR(x)=3(x-1)x2-4

02

Factor the numerator and denominator

Factoring, we get

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

03

Calculating the domain

Setting the denominator to zero, we get

(x-1)(x-2)(x+2)=0x=1,2,-2

The domain is all real numbers except1,2,-2

04

Calculate the x intercept

Calculating, we get

3not equal to zero

So no xintercept and yintercept is

R(0)=34

05

Calculating the vertical asymptote

Setting denominator to zero, we get

(x-1)(x+2)(x+2)=0x=1,-2,2is the vertical asymptote

06

Calculating the horizontal asymptote

Here the degree of numerator is less than denominator so the horizontal asymptote is y=0

The intersection point is R(x)=3x3-x2-4x+4=0

So it doesn't intersectsR

07

Sketching the graph

The graph is

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Most popular questions from this chapter

Find a rational function that might have the given graph.

Find the domain of the rational function.

G(x)=6x+34-x

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Part (b): Graph C=Cr. For what value of r is the cost C a minimum?

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