AP Calculus BC

Continuity

A function is continuous at $x = c$ when $f(c)$ is defined, $\displaystyle\lim_{x \to c} f(x)$ exists, and $\displaystyle\lim_{x \to c} f(x) = f(c)$.

A removable discontinuity is a hole, where a common factor cancels. A non-removable discontinuity is a vertical asymptote, where the denominator is $0$ and the factor does not cancel.