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Chapter 4: Q. 30 (page 234)

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

G(x)=x2-x-12x+1

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given functionG(x)=x2-x-12x+1

02

Factoring the numerator and denominator

Factoring, we get

G(x)=x2-x-12x+1G(x)=x2-4x+3x-12x+1G(x)=x(x-4)+3(x-4)x+1G(x)=(x+3)(x-4)x+1

03

Calculate the domain

Setting denominator to zero, we get

x+1=0x=-1

The domain is all real numbers except-1

04

Calculate the x intercept

Setting numerator to zero, we get

(x+3)(x-4)=0x=-3,4

Theyintercept isG(0)=-12i.e.(0,-12)

05

Calculate the vertical asymptote

The vertical asymptote is zeroes of denominator

x=-1

06

Calculate the horizontal asymptote

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

G(x)=x-2+-10x+1

y=x-2

G(x)=x2-x-12x+1=x-2x2-x-12=(x-2)(x+1)0=10

This is not true so it doesn't intersectR

07

Sketching the graph

The graph is

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Most popular questions from this chapter

Analyze each polynomial function using Steps 1through 8:

f(x)=x4-x3-6x2+4x+8.

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

Find the sum of the remaining solutions.

Graph each rational function using transformations.

R(x)=1x-1+1

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

Ct=50tt2+25

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.

Solve the inequality algebraically

(x-1)(x-2)(x-3)鈮�0
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