A continuous function is any function where there are no abrupt changes in value, these abrupt changes are called discontinuities.

Continuity at a Point

Formally for a function is said to be continuous at a point if it satisfies the following one-sided limits.

Continuity over an Interval

A function is continuous over an interval if it is continuous at every point in the interval.

Examples

Continuous

At the point the function is continuous as

Non-Continuous

At the point the function is not continuous as