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







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