If you remember, an asymptote is a limiting value which the function approaches but does not necessarily reach. There are three types of asymptotes, horizontal, vertical and slant.
A horizontal asymptote is a line y = c such that either 
or 
.
It is possible for a function to cross a horizontal asymptote.
A vertical asymptote is a line x = c such that the function f is undefined at x = c. A function can never cross a vertical asymptote.
A slant asymptote is more complicated. If y = f(x) is a rational function, the the polynomial portion of the quotient obtained through long division defines a straight line which the rational function is asymptotic to.