# How do you find the discontinuity of a function?

Apr 23, 2015

The answer to that question depends very much on the function.
In general you need to find points $a$ in the domain where
the function is defined in some open interval containing $a$, but

it is NOT true that ${\lim}_{x \rightarrow a} f \left(x\right) = f \left(a\right)$. Perhaps because one of the other (or both) fail to exist or because, although they both exist, they are distinct.

The detail vary widely depending on the function.