How do I find out what kind of asymptote a function has without a graph?

Answer 1

Purely depends on what type of asymptote you are looking for. If it's vertical, you set the denominator equations equal to 0.

If it's horizontal, you look at the top and bottom powers. If it is top heavy there are no horizontal asymptotes, If it is bottom heavy then asymptote is 0. If the powers are equal then it is the coefficient in front of each of the highest powers.

If an equation is top heavy then it may also have a slant asymptote.