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Chapter 4: Q. 27 (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-4

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionR(x)=x2+x-12x-4

02

Factoring the numerator and denominator

Factoring, we get

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

03

Calculate the domain

Setting denominator to zero, we get

x-4=0x=4

The domain is all real numbers except4

04

Calculate the x intercept 

Setting numerator to zero, we get

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

Theyintercept isR(0)=3i.e.(0,3)

05

Calculate the vertical asymptote

Setting denominator to zero, we get

x-4=0x=4

06

Calculating the horizontal asymptote

The degree of numerator is greater than denominator so there is 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

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

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

Find a rational function that might have the given graph.

In Problems 57鈥� 62, find the real zeros of f. If necessary, round to two decimal places.

f(x)=x3+19.5x2-1021x+1000.5

Solve the inequality algebraically

(x-1)(x-2)(x-3)鈮�0

True or False. If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients give rise to the horizontal asymptote.
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