
• A function $f$ is continuous at $a$ if $\lim \limits _{x \to a} f(x) = f(a)$. Implicit in this definition are three conditions for continuity of $f$ at $a$:
the function $f$ is defined at $a$,
the limit of $f(x)$ as $x \to a$ exists, and
• When a function $f$ is NOT continuous at $a$, then at least one of the three conditions above are not satisfied.