Library of Functions; Piecewise-defined functions

 

FIU has online movies to help with this topic on this page. You must have QuickTime Player, a free download, installed on your computer. book.

 

Graphing Piecewise-defined functions:

As an example, let me illustrate how to graph the following function:

 

Step 1: Graph y = x2, one of our memorized graphs.

Step 2: x < -1 to erase the part of the parabola not satisfying the inequality.

Step 3: Graph y = 1, another one of our memorized graphs.

 

Step 4: Use  to erase the part of the horizontal line not satisfying the inequality.  The point (-1, 1) is shaded because it is part of the horizontal line even though it is not part of the parabola.  For a point to lie on the graph, it need only satisfy one of the rules.

Step 5: Graph , another one of our memorized graphs.

Step 6: Since the entire graph of   has , there is nothing to erase.

Step 7: As a check, make sure the final graph passes the vertical line test.

 

 

The University of Idaho provides another online resource.  These lectures are only viewable by those with DSL or cable modems.  Real Player, a free download, is required to see these videos. The videos cover the topics below. To see the videos, go to this page and look under section 3.4.

A Library of Functions

Piecewise defined functions

 

Joliet Junior College has online videos as well.
Graph piecewise-defined functions

More online help:
Definition of piecewise functions

Graphing piecewise functions