Overview: This is an activity where students must graph transformed functions on the same graph as a parent function in order to observe what happens.
I created a set of 8 transformation cards for the 4 parent functions with 6 sets to a page. The eight transformations were left, right, up, down, skinny/steeper, wider/flatter, flip, and then more than one combination of those.
For linear, I couldn't figure out if there was a transformation for left and right so I just didn't include those. Therefore, each student should have 30 transformation cards. I labeled them Transformation 1, Transformation 2, etc so that I wouldn't give away what the transformations were and I printed each transformation on a different color of card stock which greatly helped in the sorting.
From there students had to write in the parent function names and equations on all 32 graphs...which they hated and a lot of them skipped. I thought maybe I should just type them in but since I wasn't lecturing at all, I think this was an easy way for the students to commit those four function names and equations to memory.
They then sorted and found the cards for Transformation 1 and matched them to the correct graph shape (again reinforcing what they analyzed the day before). They wrote this new equation in the 'new equation' box and graphed it on their calculator. (I plan to have students go back with a highlighter and highlight the part of the 'new equation' that is different from the original.)
Next they graphed the new equation on their calculator and sketched it with a colored pencil on the graph. Now the parent graph is already on there and I did that on purpose so they could easily see what happens to their colored graph.
Therefore, the next step was for them to finish by answering the question "What happened to the graph?" This process is repeated throughout all 8 transformations.