Overview
On this page, we discuss piecewise-defined 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 piecewise-defined function at a specific \(x\)-value.
- Recognize the domains of the different “pieces” of a piecewise defined function.
- Sketch the graph of a piecewise-defined 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 piecewise-defined functions.
- Find the domain and range of a piecewise-defined function.
To prepare for class
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Watch the following video (by ThinkwellVids, 3m47s) which explains how to evaluate a piecewise-defined function at a given specific \(x\)-value:
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Watch the following video (by The Organic Chemistry Tutor, 11m58s) which shows how to sketch the graph of a piecewise-defined function:
After class
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Watch the following video (by Cole’s World of Mathematics, 13m51s) which shows some more examples of sketching the graph of a piecewise-defined function:
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Watch the following video (by patrickJMT, 4m55s) which shows examples of finding the domain and range of a piecewise-defined function:
