What is an Asymptote?

Introduction to Asymptotes

The graph can be easily interpreted if the bounds of the graph are known. The limits which bound the function are called asymptotes. The graph of the example function C(t) is again drawn for convenience.



The asymptote of the graph in the example function C(t) where

is the x-axis. The x-axis which is written as y=0 is considered as the horizontal asymptote since the value of the function tends to zero as t tends to infinity.

Thus, an asymptote can be defined as a line that is the limiting position of a tangent to a curve as its point of contact recedes indefinitely along an infinite branch of the curve.

Types of Asymptotes

There are three types of asymptotes. They are horizontal asymptotes, vertical asymptotes and oblique asymptotes.

Horizontal asymptotes are lines of the form y = L , where L is a constant.

Vertical asymptotes are lines of the form x = L , where L is a constant.

Oblique asymptotes are lines of the form y = mx + b where m is the slope of the line and b is a constant.