**Section Objectives**

- Define and evaluate piecewise functions.
- Sketch the graph of a piecewise-defined function.

A ** piecewise-defined function** is a function defined by two or more formulas, where any particular formula is valid only for a unique portion of the function's overall domain.

For example...

When evaluating or graphing piecewise-defined functions, be sure to use only the formula that applies to the portion of the domain that is under consideration.

- Refer to the function given above. Evaluate , , and .

Consider the following function:

Sketch the graph of . Determine the domain and range of .

A function is said to be ** continuous** if its graph can be drawn without picking up your pencil. Piecewise-defined functions can be discontinuous at the break points even if the individual formulas (or pieces) define continuous functions.

Consider the following function:

Sketch the graph of . Is a continuous function?

Sketch the graph of :