Asymptote
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
An asymptote is a line that a graph of a function approaches but never actually touches or crosses. It represents a boundary that the function gets closer to as the values of x or y increase or decrease, but it never reaches it.
There is one main type of asymptote you’ll encounter in Algebra 1:
1. Horizontal Asymptote: A horizontal line that the graph approaches as x moves toward very large positive or negative values. It tells you the value that y approaches when x becomes very large or very small.
Example: In the function y = 0.5^x, the horizontal asymptote is y = 0, because as x increases, the value of y gets closer and closer to zero.
In short, asymptotes describe the behavior of a graph at the extreme ends or near specific points where the function does not have a defined value but gets infinitely close to a certain line.