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!
GeoGebraBook: Exploring Linear Functions,
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
Check out this GeoGebraBook of nine applets that will help you explore Unit Circle Symmetries. It contains three applets per type of symmetry on the unit circle, one focusing only on the unit circle, and the other two linking unit circle properties to patterns in the graphs of the sine and cosine functions.
When two angle expressions, such as and , exhibit symmetry on the unit circle, an understanding of unit circle symmetries and reference angles often allow function arguments to be simplified. Mastery of symmetries and reference angles will also be very handy when expanding inverse trigonometric function results to describe all possible answers to a problem.
Suggestions for improvements to these applets, or additional applets, are always welcome via comments on this post.
A few more interactive GeoGebra applets have been added to my collection.
Each of these graphs the function indicated in the name, with parameters that you can adjust using sliders. As you move a slider, you can watch how that parameter affects the graph of the function, and see what the resulting function definition looks like.
Each of these pages also has a set of questions following the grapher that are intended to lead students through the process of playing with and considering the effect of each constant on the graph (without giving away too much, hopefully…).
The greatest value of GeoGebra, or Geometer’s Sketchpad, or other such packages, in my eyes is their ability to help students dynamically visualize the effect each constant has on the graph of an equation. I find them an invaluable “thinking aid” as I ponder a new equation form, and they help me formulate my own answers to questions such as “why does it do that?”
Check out applets that help students explore the relationship between function parameters and their graphs:
GeoGebraBook: Exploring Linear Functions, which contains
GeoGebraBook of Quadratic Applets, which contains
Exponential and Logarithmic functions:
GeoGebraBook of Exponential and Logarithmic Applets, which contains
GeoGebraBook for Exploring Trig Functions, which contains
Unit Circle Symmetries:
GeoGebraBook of Unit Circle Symmetry applets, which contains:
Towards the end of the unit(s) on Linear Equations and their graphs, students can feel a bit overwhelmed. The following is an attempt to summarize and link the key concepts you need to be comfortable with.
What is the least amount of information you need to know in order to be able to identify a line exactly? Two pieces of information: a point that the line passes through, as well as either a second point on the line or the line’s slope.
Continue reading Analyzing Linear Equations: a summary