This learning activity allows the student to explore the vertical and horizontal asymptotes of a rational function. It also gives a graphical introduction to partial fractions.
Type of Material:
Classroom demo; student exploration
Requires a "Java-enabled" browser.
Identify Major Learning Goals:
The successful student will learn how to identify the asymptotes of a rational function and will understand the idea of partial fractions
Target Student Population:
Prerequisite Knowledge or Skills:
The activities assume no prior knowledge other than the Cartesian coordinate system, although critical thinking abilities at the Pre-Calculus level or above is needed.
Evaluation and Observation
This learning object consists of a graphing tool accompanied by five activities. On the left is a frame containing well written instructions that guide the student through the activities. The frames width can easily be resized. On the right is the graphing tool. In the activities, the student is asked to enter the equations of rational function and then explore the graphs. The equations are entered with parameters and the student is instructed to change the parameters to see how the graph is affected. The parameters can be inputted, incremented manually, or automatically so that the student can explore the effect of the graph when the parameters change. Instead of telling the student what to do, the activities ask to students to explore on their own. The concepts of vertical, horizontal, and slant asymptotes as well as partial fractions are explored.
Reformatting the left activity frame to use bulleting, numbering, or some other organizational technique would make the instructions easier to follow.
Potential Effectiveness as a Teaching Tool
The object is can be used by students learning on their own without the assistance of an instructor. The student using this activity will have the opportunity to explore the graphs of rational functions without getting frustrated. They will develop an understanding of asymptotes visually. This is especially effective for the student who learns well visually and kinesthetically. For the user who may be unsure of the expected results, summaries are provided at various intervals to keep the user on track.
The animation can be extremely quick, depending on the users computer. An additional comment that using a value of E that is negative will produce a slower graph would be helpful to the student who does not realize this in advance. In activities 2 and 5,
the there are so many graphs shown, it is difficult to see what is going on.
The variable h has multiple uses in the applet, which can be confusing to the user. The h is used as a view dimension, and in the activity directions to Plot 1/(x-h)+k.
The graph window is relatively small, making it difficult to see the detail required to reach conclusions regarding the concepts under review.
Ease of Use for Both Students and Faculty
The instructions for each of the activities are easy to follow. If the student follows the directions then there should be no difficulties in using this learning object. A help link that gives explanations on how to use the graphing tool is provided.
The parameter controls could be enlarged and separated so that they do not overlap. It would be helpful to have the Stop button present whenever the animation feature is used.
The requirement of using * to indicate multiplication is cumbersome since most graphing utilities now use syntax with implied multiplication.