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Chapter 4: Q. 20 (page 234)

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

G(x)=3xx2-1

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionG(x)=3xx2-1

02

Calculating the domain

Setting the denominator to zero, we get

x2-1=0x=卤1

The domain is all real numbers except1,-1

03

Factoring the numerator and denominator

Factoring, we get

G(x)=3xx2-1G(x)=3x(x-1)(x+1)

04

Calculate the x intercept

Setting denominator to zero, we get

3x=0x=0

G(0)=0

05

Calculate the vertical asymptote

Setting to zero, we get

x2-1=0x2=1x=卤1is the vertical asymptote

06

Calculating the horizontal asymptote

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

G(x)=3xx2-1=0x=0

So the intersection point is(0,0)

07

Sketching the graph

The graph is

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Most popular questions from this chapter

Find the real zeros off. Use the real zeros to factorf. f(x)=2x4+17x3+35x2-9x-45

The concentration C of a certain drug in a patient's bloodstream t hours after injection is given by

Ct=t2t2+1

Part (a): Find the horizontal asymptote of Ct. What happens to the concentration of the drug as t increases?

Part (b): Using your graphing utility, graph C=Ct.

Part (c): Determine the time at which the concentration is highest.

In Problems 57鈥� 62, find the real zeros of f. If necessary, round to two decimal places.

f(x)=x4+1.2x3-7.46x2-4.692x+15.2881

Solve the given inequality algebraically.

x3>1

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R(x)=1x-1+1
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