\begin{definition}[Definition:Horizontal Asymptote]
The horizontal line $y = L$ is a '''horizontal asymptote''' of the graph of a real function $f$ if either of the following limits exist:
:$\ds \lim_{x \mathop \to +\infty} \map f x = L_1$
:$\ds \lim_{x \mathop \to -\infty} \map f x = L_2$
\end{definition}