Piecewise function

Definition

A piecewise function is a function composed of multiple sub-functions, each defined on a specific interval of the domain. These sub-functions can vary in form and are typically separated by different conditions.

5 Must Know Facts For Your Next Test

1. Piecewise functions can be defined using different expressions for different parts of the domain.
2. The notation for a piecewise function often uses braces to list the distinct sub-functions and their corresponding intervals.
3. To determine the value of a piecewise function at a given point, identify which interval the point belongs to and use the corresponding sub-function.
4. Piecewise functions are useful for modeling real-world scenarios where a single formula does not apply across all inputs.
5. The domain of a piecewise function is the union of all intervals over which its sub-functions are defined.

Review Questions

• How do you evaluate a piecewise function at a given point?
• What is the general notation used to define a piecewise function?
• Can you describe how to find the domain of a piecewise function?

Related terms

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

Range: The set of all possible output values (y-values) produced by a function.

Interval Notation: A way to describe subsets of the real number line using intervals, including endpoints if specified.