# Piecewise Continuous

Learned in MATH213.

Definition 6: Piecewise Continuous

A function $f(x)$ is

piecewise-continuouson a given finite interval if

- $f$ has a finite number of discontinuities in that interval and
- for each discontinuity $x_{0}$ both the left and right hand limits exits (note they can be different values).
A function $g(x)$ is piecewise-continuous if it is piecewise-continuous on all finite intervals.

Used in the Initial Value Theorem definition.