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

Function Translations: How to recognize and analyze them

A function has been “translated” when it has been moved in a way that does not change its shape or rotate it in any way. A function can be translated either vertically, horizontally, or both. Other possible “transformations” of a function include dilation, reflection, and rotation.

Imagine a graph drawn on tracing paper or a transparency, then placed over a separate set of axes. If you move the graph left or right in the direction of the horizontal axis, without rotating it, you are “translating” the graph horizontally. Move the graph straight up or down in the direction of the vertical axis, and you are translating the graph vertically.

In the text that follows, we will explore how we know that the graph of a function like

g(x)=x^2-6x+10\\*~\\*~~~~~~~=(x-3)^2+1

can be described as a translation of the graph of

f(x)=x^2 ~~~~\text{translated right by 3, and up by 1}

Describing g(x) as a translation of a simpler-looking (and more familiar) function like f(x) makes it easier to understand and predict its behavior, and  Continue reading Function Translations: How to recognize and analyze them