Piecewise-defined functions

Definition

A piecewise-defined function is a function composed of multiple sub-functions, each defined on a specific interval of the domain. The overall function's definition changes depending on the input value.

5 Must Know Facts For Your Next Test

1. Piecewise-defined functions can be continuous or discontinuous.
2. Each sub-function has its own domain, and these domains should not overlap unless specified by the problem.
3. The notation for a piecewise-defined function often involves curly braces to separate different cases.
4. To evaluate a piecewise-defined function at a point, determine which sub-function applies to that specific input value.
5. Graphing piecewise-defined functions requires plotting each sub-function over its respective interval.

Review Questions

• How do you determine which sub-function to use when evaluating a piecewise-defined function at a given point?
• What does it mean for a piecewise-defined function to be continuous at a particular point?
• Describe the steps involved in graphing a piecewise-defined function.

Related terms

Domain:

The set of all possible input values (x-values) for which the function is defined.

Continuity:

A property of a function if it is continuous at every point in its domain; there are no breaks, jumps, or holes in its graph.

Interval: A subset of the real number line that contains all numbers between two endpoints.