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Chapter 4: Q. 22 (page 234)

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

R(x)=-4(x+1)x2-9

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionR(x)=-4(x+1)x2-9

02

Factoring the numerator and denonimator

Factoring, we get

R(x)=-4(x+1)x2-9R(x)=-4(x+1)(x-3)(x+3)

03

Calculate the domain

Setting denominator to zero, we get

(x+1)(x2-9)=0(x+1)(x-3)(x+3)=0x=-1,3,-3

The domain is all real numbers except-1,3,-3

04

calculate the x intercept

There is no term of xso there is no xintercept

TheyisR(0)=49

05

Calculate the vertical asymptote

Setting denominator to zero, we get

x=-1,3,-3

06

Calculating horizontal asymptote

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

The intersection point is

R(x)=-4x3+x2-9x-9=0-4=0

It is not true so it doesn't intersectsR

07

Sketching the graph

The graph is

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Most popular questions from this chapter

In Problems 63鈥�72, find the real solutions of each equation.

x4-x3+2x2-4x-8=0

In Problems 63鈥�72, find the real solutions of each equation.

2x3+3x2+2x+3=0

Solve the inequality algebraically.

x4<9x2

In Problems 39鈥�56, find the real zeros of f. Use the real zeros to factor f.

f(x)=2x4-3x3-21x2-2x+24

Find a rational function that might have the given graph.
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