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Chapter 4: Q. 23 (page 234)

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

H(x)=x2-1x4-16

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionH(x)=x2-1x4-16

02

Factoring the numerator and denominator

Factoring, we get

H(x)=x2-1x4-16H(x)=(x-1)(x+1)(x2-4)(x2+4)H(x)=(x-1)(x+1)(x-2)(x+2)(x2+4)

03

Calculate the domain

Setting the denominator to zero, we get

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

The domain is all real numbers except2,-2

04

Calculate x intercept 

Setting numerator to zero, we get

x2-1=0x=1,-1

Theyintercept isH(0)=116

05

Calculating the vertical asymptote

The degree of numerator is less than denominator so the vertical asymptote is x=2,-2

The horizontal asymptote is y=0

H(x)=x2-1x4-16=0x2-1=0x=卤1

It intersects at(-1,0),(1,0)

06

Sketching the graph

The graph is

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Most popular questions from this chapter

Find the domain of the rational function.

R(x)=5x23+x

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

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

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

One solution of the equation x3-8x2+16x-3=0 is 3.

Find the sum of the remaining solutions.

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

f(x)=4x4+7x2-2
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