Line in which the distance to any given point of a curve tends toward zero when this point moves away on the curve infinitely (in the positive or negative direction of the independent variable).

### Properties

A horizontal asymptote is a line that is parallel with the *x*-axis.

A vertical asymptote is a line that is parallel with the *y*-axis

### Examples

### Historical Note

The terme “asymptote” comes from the Greek word “*asumptotos*” which means “not falling together”.