## 6.2. Continuous Functions

### Definition 6.2.2: Continuity

A function is

**continuous at a point***c*in its domain*if: given any***D***> 0*there exists a*> 0*such that if*x*and**D***| x - c | <*then*| f(x) - f(c) | <*.
A function is **continuous in its domain** * D* if
it is continuous at every point of its domain.

This, like many *epsilon-delta* definitions and arguments, is
not easy to understand. Click on the `Java` icon to see an
applet that tries to illustrate the definition.