Infinite Discontinuity

A third, more dramatic way a function can fail to be continuous is by growing without any bound at all as $x$ approaches the point — there is then no finite height the graph is settling towards, from one side or both. This is called an infinite discontinuity:

$\textbf{A function } f(x) \textbf{ is said to have an infinite discontinuity at } x=a \textbf{ if } \lim_{x\to a^-} f(x)=\pm\infty \textbf{ or } \lim_{x\to a^+} f(x)=\pm\infty.$ …