Desmos to demonstrate transformations, reflections

Did you know that if you type in a function using f(x) =     then you can type  -f(x) to show a reflection.  In my last post, I was doing this manually without using f(x) notation.   So to show the graph a function translated to the left 5 units and down 2units,  you would use  the notation f(x+5)-2

What a powerful teaching tool for the teacher to demonstrate translations, reflections and dilations!  putting the graphs that are color coded to the equation in projexpctor mode shows the function notation and the visual of what each number does to the graph!

Using Geogebra to Verify if a function is odd, even or neither

In a PreCalculus or Calculus class, students often struggle to see how the definition of an even or odd function fits the mathematical definition.

To remind the student, a function is odd if it fits this definition:   f(-x)= -f(x)    Graphically, this means that for every point (x,y) belonging to the function,  then (-x, -y) is also a point on this same function.  This will appear in a graphing calculator as a function with point symmetry about the origin.  The first quadrant will map to the third quadrant; the second quadrant to the fourth - and the curve will be inverted.


A function is even if it fits the definition:  f(-x) = f(x)   This means that the y value associated with each distinct x is the same y value for the opposite of x.   This will appear in a graphing calculator as a function that is symmetrical to the y axis as  -x has the same height (y) as x does.

For the past 6 years, I have been using Geogebra to illustrate complex mathematical topics.  Here are some screenshots from a demonstration that the function   f(x)=x^4+x^2  is an even function and not an odd function.     g(x)=-f(x)  and h(x)=f(-x)

In the screenshot below you can visually see the f(-x)  *shown in red  does not equal  -f(x)  so it is NOT odd.

In this screenshot below you can visually see that  f(-x) = f(x) since the two graphs are superimposed and the conclusion is this function is even. 

Solving Absolute Value Inequalities visually and algebraicly

Solving absolute value inequalities often is very misunderstood by our students.  I know several textbooks lay out four different scenarios in a table that students often try to memorize and then misuse or misapply.  Here is a simple technique that relies on logic and visualization to solve them (but be prepared, there is a quiz at the end!) This is my own creation for a technique that I use in my classroom using endpoints and regions.  The video was produced using Smart Notebook software capture in Camtasia Studio. Click on this link:  Absolute Value Inequalities - a visual approach

Finding the inverse of a given function

How to find the inverse of a given function (in 2 parts)  Part 1 Introduction

For teachers interested in how this presentation was created:  I used an IPad App: ExplainEverything which is a whiteboarding app that allows recording and interactivity along with audio.  I created two MP4's that were then uploaded to dropbox for further processing and also uploaded the videos to YouTube.

ExplainEverything Website for more information

I then imported the two MP4s into a Camtasia project on a PC so that I could combine them, do some minor audio editing (by separating the audio from the video)  and finally produced an edited version that had online quizzing.  The results of the quiz are then sent to my email address.  If you would like to see the edited version with the online quizzing:

More Walking Dead Projects

This post was deleted because the next year's students are now engrossed in the project.

Geometry Pad Plus - Reviewed

Another math app to consider adding to your Ipad is Geometry Pad Plus. Here is a short video I made describing it:

Posted with Blogsy

Zombie Apocalypse ... the aftermath!

It's the following year from the initial post and I had to delete the information here because a whole new set of students are working on this project!