Second, to find vertical asymptotes, set the denominator equal to zero.
For slant asymptotes if the numerator is one degree higher than the denominator, do the long division. The linear and constant terms of the result is the slant asymptote.
For horizontal asymptotes the degree of the numerator is the same or less than the degree of the denominator. What happens when x is very large and negative? when x is very small and negative?
There are no other kinds of asymptotes, so this covers everything.