Maggie (@pitoinfinity8) posted an awesome activity for piece-wise functions in which students literally cut up the different pieces of a given function and then puzzle them together. Brilliant. In response, Bowman Dickson mentioned that it might be useful to go the other way, too; in other words, give the students the graph and have them write the equation.
I love both these ideas: the first gets the students to read; the latter gets them to write. I didn't read Maggie's post until after I introduced piece-wise functions this year in Pre-Calc, but I did read it in time for our first test review.
So, here's what we did...
I gave them a few minutes to answer these questions and then we used their answers along with the restrictions to write the function.
Onto another one:
They were rockin and rollin, so I asked them...
This time, I gave them the problem in the traditional manner:
Success! Finally! Many thanks to Maggie and Bowman. What a great way to review both piece-wise functions and function transformations.
Speaking of function transformations, a twitter conversation in which I laughed out loud: