Definition:Horizontal Asymptote

Definition
The horizontal line $y = L$ is a horizontal asymptote of the graph of a real function $f$ if either of the following limits exist:


 * $\displaystyle \lim_{x \to +\infty} f\left(x\right) = L_1$


 * $\displaystyle \lim_{x \to -\infty} f\left(x\right) = L_2$

If $L_1$ and $L_2$ both exist and $L_1 \ne L_2$, the graph of $f$ has two horizontal asymptotes.

Also see

 * Vertical Asymptote
 * At Most Two Horizontal Asymptotes