Exponential Models Card Sort

Thanks to the ever-innovative-and-tuned-in-to-what-teachers-would-love-to-have Desmos team, I've created an online version of a card sort that I originally developed in paper form to help precalculus students think carefully about the meaning of the parameters in various forms of exponential equations. See this blog post for more detail on the context in which I use this.

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.

Napier's Gift

I was inspired by the first chapter of Eli Maor's e:The Story of a Number to create this GeoGebra applet designed to help the user discover how to simplify the process of finding a quotient by subtracting exponents. The idea is both to introduce students to logarithms (though they are never mentioned explicitly) and to help students understand why they were so heralded when they were introduced. The applet is also posted on GeoGebraTube.

Connecting exponential equations and their graphs

This is a Geogebra applet created by Steve Phelps in which you construct the graph of an exponential function by placing the asymptote, the y-intercept and one other point. You then type in what you think the graph of your equation ought to be. The equation you type in is graphed so you can see if you're right.