key term - Continuous

Definition

A function is continuous if there are no breaks, holes, or jumps in its graph. In other words, you can draw the entire graph without lifting your pen.

5 Must Know Facts For Your Next Test

1. A polynomial function is always continuous.
2. Continuity at a point means the function's value at that point equals the limit of the function as it approaches that point.
3. If a function is not continuous at a point but has a limit that exists, it may have a removable discontinuity.
4. Rational functions can be discontinuous where their denominators are zero.
5. The Intermediate Value Theorem applies to continuous functions over an interval.

Review Questions

Related terms

Intermediate Value Theorem:

If a function is continuous on [a, b], then it takes on every value between f(a) and f(b).

Removable Discontinuity: A point at which a graph is not connected but can be made continuous by redefining the function.

Limit:

The value that a function approaches as the input approaches some value.