Transformations on a Graph
I've been looking for Geogebra applications for function transformations, and wanted to share a couple of the neat sketches I've found.
Michael Higdon, a math teacher at Kincaid, a college prep school in Texas, has a quadratic function in vertex form, y=a(x-h)^2+k, with a, h and k as sliders to study transformations.
Geogebra webpage: Transformation of Functions
Mike May, a Jesuit math teacher at St. Louis University, has a beautiful applet where you can input the function, and control vertical and horizontal shifts and scaling with sliders.
Geogebra webpage: Translation Compression
An overall great collection of interactive webpages appears at The Interactive Mathematics Classroom. It has a nice search feature and a good breakdown by area of mathematics.
My first attempt at a transformations sketch is with a cubic as the starting function. Although you can change the function.
As a webpage, and as the geogebra file.
Slope in Linear Equations
A nice collection of middle school or Algebra I activities for linear equations from mathcasts.org: Slope Explorations
Mathcasts are screencasts of writing with voice-overs. They have mathcasts for K-12, and a nice collection of interactive math activities.
Here's my first slope sketch. It tries to get at the idea of the slope being constant on a line regardless of what points are selected.
As a webpage or a geogebra file.