So I wanted to share an activity I did for function transformations and piecewise functions (well, maybe more exploring domain restrictions that are used in piecewise functions)
Since I know this post will be shared with some of my non-math friends from Pinnacle, I'll give you a bit of background (hopefully in language that's as non-mathy as possible.)
Our Math 2 students are supposed to learn different types or classifications for equations (functions). They also learn to "move" the graphs of those equations by changing different parts of the original function's equation. (For example, they can add to the end of an equation to move it up on the graph).
Here's what we did:
1) Students created a drawing of their choosing in Desmos (an online graphing calculator).
They were instructed to include 4 linear, 1 absolute value, 1 exponential, and 1 quadratic equation. They were required to have a minimum of 15 components of their graph, including no more than 4 horizontal or vertical lines. They were encouraged to be creative.
2) After creating and saving their graph in Drive, they shared it with me, so I could grade the equations.
3) Then they took a screenshot of their graph, and imported it into skitch. They used the app to label a minimum of 7 of the 15 components. Then they sent the skitch image to me.
It was a great, quick (2-day) activity that lead to some AWESOME conversations. It was also really interesting to see the shapes they could create from certain functions by changing the scale of their graph, or only using a certain piece of that function. Cool stuff.
Here are some of the skitch images (I'm not sharing the equations files because I know so many of my secondary friends do similar projects, and I don't want to create opportunities for cheating). There is one file below that included that in the screenshot, so you can see generally what they were creating for the equations.