Vertical Asymptotes -- Basic Rules

A rational function f(x) = p(x) / q(x) may have a vertical asymptote x=a only if the denominator, q(x), is zero at x=a .
If the denominator is 0 at x=a, and the numerator is different from 0 at x=a, then f(x) does have a vertical asymptote at x=a .

Horizontal Asymptotes -- Basic Rules

Consider a rational function f(x) = p(x) / q(x)

1. If the degree of p(x) is equal to the degree of q(x), then
                                y=a_n / b_n
is a horizontal asymptote, where a_n and b_n are leading coefficients of p(x) and q(x), respectively.

2. If the degree of the denominator, q(x), is larger than the degree of the numerator, p(x), then y=0 is a horizontal asymptote.

3. If the degree of the denominator, q(x), is less than the degree of the numerator, p(x), then f(x) has no horizontal asymptote. (It may have a slant asymptote.)