# Find the Asymptotes f(x)=(x^2-64)/(x-8)

Find where the expression is undefined.
The vertical asymptotes occur at areas of infinite discontinuity.
No Vertical Asymptotes
Consider the rational function where is the degree of the numerator and is the degree of the denominator.
1. If , then the x-axis, , is the horizontal asymptote.
2. If , then the horizontal asymptote is the line .
3. If , then there is no horizontal asymptote (there is an oblique asymptote).
Find and .
Since , there is no horizontal asymptote.
No Horizontal Asymptotes
Find the oblique asymptote using polynomial division.
Simplify the expression.
Simplify the numerator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
The oblique asymptote is the polynomial portion of the long division result.
This is the set of all asymptotes.
No Vertical Asymptotes
No Horizontal Asymptotes
Oblique Asymptotes:
Find the Asymptotes f(x)=(x^2-64)/(x-8)