Objectives:
1. Define continuity of a function (from the left, from the right, at a point, and over its domain).
2. Determine if a function is continuous at a point or on its domain.
3. Describe three kinds of discontinuities.
4. Define continuity on an interval.
5. State the theorem for limits of composite functions.
6. Provide an example of the intermediate value theorem.
Many functions have the property that their graphs can be traced with a pencil without lifting the pencil from the page. Such functions are called continuous. Other functions have points at which a break in the graph occurs, but satisfy this property over intervals contained in their domains. They are continuous on these intervals and are said to have a discontinuity at a point where a break occurs.