This interactive, applet-based site steps the student through the process of finding the domain of a function constructed from polynomials, and roots and ratios thereof. New problems are generated at the click of a button. Feedback and hints are provided along the way, and links are provided to pages providing explanations of the concepts and techniques involved.
This site is designed to facilitate understanding of the concept of domain of a function, and of some of the reasons a functions domain may fail to be the set of all real numbers.
Target Student Population:
This site would be useful in either a high school or college algebra class.
Prerequisite Knowledge or Skills:
The student should be familiar with the concepts of function and domain.
Type of Material:
This site would best be used as the basis for a homework assignment or in an instructor-led discussion.
A Java-enabled browser is necessary.
Evaluation and Observation
There are no apparent mathematical flaws in this site, either in the applet or the linked explanatory pages. The random problem generator works well, generating functions with a variety of domain types (infinite, semi-infinite, finite, with and with endpoints, with and without a single-point hole in the interior). The hints provided as a result of an erroneous response were carefully constructed and are very helpful in directing the user to the correct solution.
Potential Effectiveness as a Teaching Tool
The major strengths of this site are the graphical, step-wise nature of the required domain determination procedure, and the effective feedback and hints provided during the procedure. The hints go beyond right or wrong, try again. A typical hint might read Notice the inside of the root is positive for large negative values of x. This is both more useful and more thought-provoking than a simple wrong.
Enhancing the effectiveness of this site is the existence of an associated assignment created by two other authors.
Not so much a concern as a suggestion this is such a nice applet that it would be nice to have another one that incorporates other functions (logarithms, exponentials, trig functions, complex Hankel functions of the second kind, etc.)
Ease of Use for Both Students and Faculty
Using the applet could not be easier. Instructions are simple and clear. Everything works with the click of a mouse.