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Chapter 4: Q. 19 (page 234)

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

G(x)=xx2-4

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given the functionG(x)=xx2-4

02

Factoring the numerator and denominator

Factoring, we get

G(x)=xx2-4G(x)=x(x-2)(x+2)

03

Calculate the domain

On setting the denominator to zero, we get

x=2,-2

So the domain is all real numbers except2,-2

04

Substitute numerator equal to zero to get the xintercept 

Substituting, we get

x=0

So the xintercept is zero so theyintercept is0

05

Calculate the vertical asymptote

Setting denominator to zero, we get

x2-4=0x=2,-2is the vertical asymptote

06

Calculating the horizontal asymptote

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

The intersection point is G(x)=xx2-4=0

So the point is(0,0)

07

Sketching the graph

The graph is

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Most popular questions from this chapter

In Problems 21鈥�32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=-4x3-x2+x+2

Analyze each polynomial function using Steps 1through 8:

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

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

f(x)=4x5+12x4-x-3

Find the domain of the rational function.

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R(x)=5x23+x
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