The word asymptote is derived from the Greek means "not falling together".
There are three kinds of asymptotes:
For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞.
Vertical asymptotes are vertical lines near which the function grows without bound.
An oblique asymptote has a slope that is non-zero but finite, such that the graph of the function approaches it as x tends to +∞ or −∞.
There are curve asymptotes believe it or not. A curve is a curvilinear asymptote of another (as opposed to a linear asymptote) if the distance between the two curves tends to zero as they tend to infinity, although the term asymptote by itself is usually reserved for linear asymptotes.
Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph.
The study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis.