# 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 −∞.

- For curves given by the graph of a function
*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 −∞.

- An oblique asymptote has a slope that is non-zero but finite, such that the graph of the function approaches it as

- 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.

## Essential Questions

Essential Questions

### How are limits related to asymptotes?

How are limits related to asymptotes?

## Practice Problems

Practice Problems