Definition: Horizontal Asymptotes
The horizontal asymptote of an equation is the long-term behavior of an equation. So, for very, very, very large values of x (i.e. ) , what does it look like your equation would head towards.
You find horizontal asymptotes by taking the limit of an equation as x approaches , and as x approaches .
and
Note:
– The answer to a horizontal asymptote question is always the that the equation is heading towards.
– You can have at most 2 horizontal asymptotes. One heading towards and one heading towards , and they are not always the same value.
– Your equation is allowed to cross the horizontal asymptote.