Piecewise functions

Definition

A piecewise function is a function defined by multiple sub-functions, each of which applies to a specific interval of the main function's domain. These functions are often used to describe situations where a rule or relationship changes based on the input value.

5 Must Know Facts For Your Next Test

1. Piecewise functions can be continuous or discontinuous depending on whether the sub-functions connect smoothly at their boundaries.
2. Each sub-function has its own domain, and these domains do not overlap.
3. When graphing a piecewise function, it is essential to use open or closed dots to indicate whether endpoints are included in each sub-function.
4. The notation for piecewise functions typically includes curly braces that list the different sub-functions along with their respective intervals.
5. Evaluating a piecewise function involves determining which sub-function applies to the given input value and then using that sub-function for calculation.

Review Questions

• What are the steps to evaluate a piecewise function at a given point?
• How can you determine if a piecewise function is continuous at a boundary point?
• Describe how you would graph a piecewise function with three different sub-functions.

Related terms

Domain: The set of all possible input values for which a function is defined.

Continuous Function: A function without breaks, jumps, or holes in its graph.

Interval Notation: A method of writing subsets of the real number line by specifying the start and end points of intervals.