Overview
On this page, we discuss piecewisedefined functions, which are functions which consist of several pieces which one can think of being cut out from other functions and then glued together.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
 Evaluate a piecewisedefined function at a specific \(x\)value.
 Recognize the domains of the different “pieces” of a piecewise defined function.
 Sketch the graph of a piecewisedefined function by splitting the coordinate plane into vertical “slices” and drawing each piece of the function only in the corresponding slice.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
 Sketch the graph of more complicated piecewisedefined functions.
 Find the domain and range of a piecewisedefined function.
To prepare for class

Watch the following video (by ThinkwellVids, 3m47s) which explains how to evaluate a piecewisedefined function at a given specific \(x\)value:

Watch the following video (by The Organic Chemistry Tutor, 11m58s) which shows how to sketch the graph of a piecewisedefined function:
After class

Watch the following video (by Cole’s World of Mathematics, 13m51s) which shows some more examples of sketching the graph of a piecewisedefined function:

Watch the following video (by patrickJMT, 4m55s) which shows examples of finding the domain and range of a piecewisedefined function: