# What are the three conditions for continuity at a point?

A function $f \left(x\right)$ is continuous at a point $\left(a , b\right)$ if and only if:
• $f \left(a\right)$ is defined;
• ${\lim}_{x \rightarrow a} f \left(x\right)$ is defined; and
• ${\lim}_{x \rightarrow a} f \left(x\right) = b$