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Chapter 4: Q. 46 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.

G(x)=x3+1x2-5x-14

Short Answer

Expert verified

y=x+5 is the oblique asymptote for the given rational expression.

Step by step solution

01

Step 1. Given information

Given rational expression:

G(x)=x3+1x2-5x-14

02

Step 2. Write the concept

If n = m + 1 (the degree of the numerator is one more than the degree of the denominator), the

quotient obtained is of the form ax + b (a polynomial of degree 1), and the line y = ax + b is an oblique

asymptote.

03

Step 3. Calculation

Here,n=3,m=2

Thus, n=m+1and therefore,

y=ax+bwillbetheobliqueasymptotey=x+5

i.e. the quotient when we divide numerator with denominator.

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Most popular questions from this chapter

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

G(x)=x3+1x2+2x

Find the domain of the rational function.

Qx=-x1-x3x2+5x-2

Find the domain of the rational function.

-4x2x-2(x+4)

Solve each inequality algebraically.

x-3x+1>0

Graph each rational function using transformations.

R(x)=x-4x
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