# Asymptotes

In analytic geometry, an

**asymptote**of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the*x*or*y*coordinates tends to infinity.In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity.

The word asymptote is derived from the Greek means "not falling together".

There are three kinds of asymptotes:

*horizontal*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*Vertical asymptotes are vertical lines near which the function grows without bound.

*oblique*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.