Piecewise Functions

By: Kate Albertini, Katie Fairman, and Anne Kaufmann

What is a Piecewise Function?A piecewise function is an equation with

multiple parts in which each part matches up with a different part of the domain.

How to Graph a Piecewise Function1) Write all of the equations of the piecewise

functions in y = mx + b form2) Look at your first equation and its domain.

Graph your first equation over that domain.3) Put a closed circle on the beginning or ending

points if that point is included in the domain (greater than or equal to, less than or equal to). If the point is not included in the domain, use an open circle (less than or greater than).

4) Repeat for the other equations of the function.

An ExampleThe solid part of each line represents the part of the line defined by the piecewise function. The dotted part of the line shows the rest of the line which is not included in the piecewise function.

Step FunctionA step function is a specific kind of piecewise

function in which the different parts of the equation look like steps when graphed.

All rules for piecewise functions still apply.

An Example