Graph Transformations of Functions
Graph Transformations, I think are personally taught best by guided student discovery
with either a little or a lot of detail involved depending on the students. In some cases,
it could be necessary, as students are discovering graph transformations to have them write
out different points x and y to see how a transformation affects the points. Another tip
might be to have students draw the original graph and then sketch the transformed graphs.
Both of these ideas can be used when having student discovery graph transformations for
themselves rather than just being told the easily interchangeable rules. Below I have linked
some videos about the basics of graph transformations review is needed but I invite you to use
the video below to create a geogebra applet that will allow you to make these discoveries for yourself.
Resources for Learning Simple Function Transformations
Original YouTube Video-Graph Transformations (there is no sound at the moment sorry)
Math Is Fun- Overview of Function Tranformations
Khan Academy Video-Shifting and Reflecting Functions
Purple Math-Overview of Function Transformations
Real Life Applications of Function Transformations
Some of my favorite kinds of transformations come from art, Native American and African American arts.
Many of their beautiful designs integrate the mathematics of translation, transitivity and are reflexive.
(Here is a lesson about translation, transitivity and reflexivity that I modified to include the art.)
This is just one example, another use of transformations, that may surprise you are computer animations
used to make some of our favorite disney movies. Computer animators use stretching, compressing, translating
(shifting left, right, up and down) in their animations of characters. Think of that next time you are watching
Frozen! I have also included an introductory paper here of a school that actually combined a computer animation
class with emphasizing some of these graph transformations. Furthermore, a Pixar employee gave talk on TED EX about
the 'Math Behind the Movies' and demonstrates how some of these graph transformations using one of our favorite characters,
Woody.
The Math Behind the Movies
Link to Class Example of Computer Animation & Graph Transformation