three-part test for continuity

$f(x)$ is continuous at $x=c$ iff

1. $f(c)$ exists,
2. ${\lim }_{x\to c}f(x)$ exists ¹, and
3. ${\lim }_{x\to c}f(x)=f(c)$

Footnotes

1. one-sided limit is acceptable when the graph ends at $x=c$ ↩