What is Asymptotes?

The line $y = \ell$ is a horizontal asymptote of the curve of $f$ at $+\infty$ (resp. $-\infty$) if $\lim_{x\to+\infty} f(x) = \ell$ (resp. at $-\infty$). The line $x = a$ is a vertical asymptote if $f$ has an infinite one-sided limit at $a$.