I can't remember where I found this activity...it was a very long time ago. I'm old :) In the past, I would cut up the pieces and have students draw the graphs on a sheet of paper. Well - in walks Desmos Activity Builder! One of the best things to happen to my classroom! Like most math teachers out there, you know what I'm talking about. So here's the gist - students create any type of graph but must meet all of the requirements. For example: (#1 The function has a limit as x approaches 2 of 5, but f(2) = -1.) I give extra points for more difficult functions. Some students get really creative while others just do the bare minimum. Before they start, the students do a small tutorial on how to set restrictions for the piecewise functions and how to turn a point into a hole. I still got a lot of questions, but some students have never seen Desmos. (Can you believe that?) The majority of students do it correctly by making piecewise functions, rational functions