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Chapter 4: Q. 53 (page 225)

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

G(x)=x4-1x2-x

Short Answer

Expert verified

The given rational expression does not have a horizontal or oblique asymptote.

Step by step solution

01

Step 1. Given information

Given rational expression:

G(x)=x4-1x2-x

02

Step 2. Write the concept

If n鈮�m+2(the degree of the numerator is two or more greater than the degree of the denominator),

the quotient obtained is a polynomial of degree 2 or higher, and R has neither a horizontal nor an oblique

asymptote. In this case, for very large values of x, the graph of R will behave like the graph of the

quotient.

03

Step 3. Calculation

heren=4,m=2

Thus,n鈮�m+2

Therefore no horizontal or oblique asymptote.

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