After the Zombie exponential problem, several students wanted to know WHAT was this mysterious LOG thing and especially why it worked? Enter, inverse functions.
I made an Inverse Functions guided worksheet for my students. It is self-directed and has them use two different colors for the graphs. They can get through the entire sheet without much help, and make all sorts of great discoveries on their own. I blew it in the first class I taught by trying to go over the sheet with them way too soon after handing it out. I wanted to explain a couple of things before they got too far. DON’T DO THAT. Give them ample time to read it, graph things, make small mistakes, and discover. It makes a huge difference not only in understanding, but in their engagement and attitude. They really don’t want to hear me talk. Instead, play music in the background, walk around and see their work, even answer a FEW of their questions. It is so good for them to work on their own!
After we went over the worksheet together, we played with the awesome inverse graph created by Desmos that I modified with the equation y=2^x. The kids can move the slider and it shows the point and its inverse on each graph!