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Chapter 4: Q. 43 (page 234)

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

f(x)=x+1x3

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionf(x)=x+1x3

02

Factoring the numerator and denominator

Factoring, we get

f(x)=x+1x3f(x)=x4+1x3

03

Calculate the domain

Setting the denominator to zero, we get

x3=0x=0

The domain is all real numbers except0

04

Calculate the x intercept

Setting numerator to zero, we get

x4+1=0x4=-1

There is nox,yintercept

05

Calculate the vertical asymptote

The zeroes of denominator is x=0so the vertical asymptote isx=0

06

Calculating the horizontal asymptote

The degree of numerator is greater than denominator so there is an oblique asymptote

f(x)=x+1x3

The oblique asymptote is y=x

f(x)=x4+1x=xx4+1=x2x4-x2=-1

It doesn't intersectsf

07

Sketching the graph

The graph is

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Most popular questions from this chapter

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

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

Solve the inequality algebraically.

x4>x2

Find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f.

f(x)=2x3-x2-11x-6

True or False The graph of a rational function may intersect a vertical asymptote.

Graph each rational function using transformations.

R(x)=x-4x
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