Interactive Graphs for Linear, Quadratic, Rational, and Trig Functions Moved to GeoGebraTube

Some may have had trouble using my GeoGebra applets in their browsers. I have moved all of them to GeoGebraTube, which will hopefully fix the problem. You may search for them by typing “MathMaine” into the GeoGebraTube search box.

Links to all updated interactive graph applets are below. Comments and suggestions are always welcome!

Linear Functions

GeoGebraBook: Exploring Linear Functions, which contains:

Interactive Linear Function Graph: Slope-Intercept Form

Interactive Linear Function Graph: Point-Slope Form Continue reading Interactive Graphs for Linear, Quadratic, Rational, and Trig Functions Moved to GeoGebraTube

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Function Dilations: How to recognize and analyze them

This post explores one type of function transformation: “dilation”. If you are not familiar with “translation”, which is a simpler type of transformation, you may wish to read Function Translations: How to recognize and analyze them first.

A function has been “dilated” (note the spelling… it is not spelled or pronounced “dialated”) when it has been stretched away from an axis or compressed toward an axis.

Imagine a graph that has been drawn on elastic graph paper, and fastened to a solid surface along one of the axes. Now grasp the elastic paper with both hands, one hand on each side of the axis that is fixed to the surface, and pull both sides of the paper away from the axis. Doing so “dilates” the graph, causing all points to move away from the axis to a multiple of their original distance from the axis. As an example of this, consider the following graph:

Vertical Dilation (no Translation)

The graph above shows a function before and after a vertical dilation. The coordinates of two Continue reading Function Dilations: How to recognize and analyze them