What You Don't See...
Objective:  This graphing calculator based demo illustrates that conclusions we make about the domain and/or range of a function using the graph only may not be accurate.  Because of limitations in how the calculator plots points in the function mode, it is important to make an analytic investigation of domain PRIOR to interpreting a calculator-generated graph.

Level:  This demo is appropriate College Algebra, Precalculus, or any course in which graphing calculators are used for graphing functions.

Prerequisites:  Students should have basic graphing calculator skills.  In the examples, a TI-85 was used to produce the graphs.  (Results are similar when using a TI-83 or TI-89.)

Equipment:  You will need a graphing calculator and either a display device for the calculator or screen capture utility so that calculator graphics may be printed to a transparency.

Instructor's Notes:

Example 1:  Plot the graph of  and give the domain.
• Using the indicated graphing window, obtain the graph.
• Use the graph to discuss the domain of the function.

• Using the graph and the trace feature on the calculator to estimate the domain, it appears that the domain does not include values of x close to -3.

Demonstrate that an analytic examination of the function shows that the domain is [-3,Infinity).

• Discuss what happened.  Is the calculator wrong?

• A look at the table generated by the function using the table settings below indicate that the calculator is computing the function values correctly: the points are just not being plotted on the graph.  The ERRORs occur outside the domain of the function.

Using the table, it is evident that the calculator is computing function values for x CLOSE to -3, however, the calculator does not display the corresponding points on the graph.

Example 2:
• Discuss the domain of the function.
• Plot the graph of .  Discuss.

Reference
Hornsby, John and Lial, Margaret L. A Graphical Approach to College Algebra, Second Edition, Addison-Wesley, Reading, 1999.

Credits:  This demo was submitted by

Dr. Lila F. Roberts
Clayton State University

and is included in Demos with Positive Impact with her permission.

Created 12/21/1999 LFR.     Last updated 9/15/2010 DRH.
Counter information prior to 2/2/2005 was lost.

Visitors since 2/2/2005