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Chapter 4: Q. 42 (page 234)

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

f(x)=2x2+16x

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionf(x)=2x2+16x

02

Factoring the numerator and denominator

Factoring, we get

f(x)=2x2+16xf(x)=2x3+16x

03

Calculate the domain

Setting denominator to zero, we get

x=0

The domain is all real numbers exceptx=0

04

Calculate the x intercept 

Setting the numerator to zero, we get

2x3+16=0x3=-8x=-2

There is noyintercept asf(0)=undefined

05

Calculating the vertical asymptote

The zeroes of denominator are 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)=2x2+16x

So y=2x2is the oblique asymptote

f(x)=2(x+2)x2-2x+4x=2x22(x+2)x2-2x+4=2x2(x)2x3+16=2x30=-16

So it doesn't intersectf

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

Find a rational function that might have the given graph.

One solution of the equation x3+5x2+5x-2=0 is -2.

Find the sum of the remaining solutions.

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)=2x5-x4-x2+1

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

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