Piecewise-defined function

Definition

A piecewise-defined function is a function composed of multiple sub-functions, each defined over a specific interval of the domain. These sub-functions can be different expressions that apply to different parts of the domain.

5 Must Know Facts For Your Next Test

1. Piecewise-defined functions often use conditional notation to specify which sub-function applies to which part of the domain.
2. Graphing a piecewise-defined function involves graphing each sub-function over its respective interval and ensuring continuity or noting points of discontinuity.
3. To evaluate a piecewise-defined function at a given point, determine which interval the point falls into and use the corresponding sub-function.
4. Piecewise functions can be used to model real-world situations where a rule changes based on different conditions or intervals.
5. Continuity and differentiability of piecewise-defined functions depend on the behavior at the boundaries between intervals.

Review Questions

• How do you determine which sub-function to use when evaluating a piecewise-defined function at a specific point?
• What are common indicators in the notation of a piecewise-defined function that show where one sub-function ends and another begins?
• How would you graphically represent each segment of a piecewise-defined function?

Related terms

Interval: A range of values in which a certain condition holds true, often denoted using inequalities.

Continuity:

A property of functions where they are unbroken or uninterrupted; specifically, there are no abrupt jumps or holes in their graph.

Sub-function: An individual function that is part of a larger piecewise-defined function, applicable over a specific interval.