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Chapter 4: Q. 40 (page 234)

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

f(x)=2x+9x

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionf(x)=2x+9x

02

Factoring the numerator and denominator

Factoring, we get

f(x)=2x+9xf(x)=2x2+9x
03

Calculate the domain

Setting denominator to zero, we get

x=0

The domain is all real numbers except0

04

Calculate the x intercept

Setting numerator to zero, we get

2x2+9=0x2=-92

There is nox,yintercept

05

Calculate the vertical asymptote

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

06

Calculating the horizontal asymptote

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

f(x)=2x+9x

y=2xis the oblique asymptote

f(x)=2x2+9x=2x2x2+9=2x20=-9

So it doesn't intersectf

07

Sketching the graph

The graph is

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