Asymptotes of Rational Functions.

Asymptotes of Rational Functions is a GeoGebra construction designed to help people explore the relationship between the equation of a rational function and its graph. You choose the rational function you'd like to explore. Here's a story of something neat that happened when I used it in class.

Finding Equations of Polynomial and Rational Functions

I created this activity with Desmos. Graphs of several polynomial and rational functions are provided. The goal is to find the equation of each. It's self-checking in that when you type in the right equation your graph will match the given graph.

Transforming f into g

Note: If you're not seeing both graphics windows on GeoGebraTube, you can download the applet and run it on your desktop.

In this applet (inspired by Steve Phelps' What's My Rule series) you select a parent function, f(x),  from among 10 possibilities and click a button to indicate the maximum number of transformations (up to 4) that you'd like to have performed on f to produce a new function g. You see only one point on g, but you can move the corresponding point on f, to determine the relationship between the two. When you believe you have found the parameters that describe the transformation, you can show the graph of the transformed function that your parameters create and see if the lone point moves along it.

Here's a Java version of the applet.

Rational Function Graphs

Use this demonstration from the Wolfram Demonstrations Project to explore the graphs of rational functions. Predict whether the function will have any holes and then check "show holes" to see if you're right. (To interact with it online you'll need to download and install Wolfram's free CDF Player.)