# Section 3.4 - Piecewise-defined Functions

Section Objectives

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

### Piecewise Functions

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.

#### Examples

• Refer to the function $f$ given above. Evaluate $f(0)$, $f(-5)$, and $f(3)$.

• Consider the following function:

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

### Continuity

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.

#### Examples

• Consider the following function:

Sketch the graph of $h$. Is $h$ a continuous function?

• Sketch the graph of $f$: