For a while now, I’ve been intrigued by the ways in which the study of geometric transformations can provide students with a very effective introduction to function concepts. Daniel and I have written a couple of articles about this topic, and we created a number of activities to take advantage of what can arguably be the most visual and tactile functions that students ever have the opportunity to experience.

In our presentation at last April’s NCTM Annual Meeting, we took this approach one step further, by proposing a sequence of student experiences that would connect the commonly-studied geometric transformations directly to linear functions in the form f(x) = mx + b, and by extension to a variety of other algebraically-expressed functions.

Though our proposed student experiences are not yet fully fleshed out, we’re eager to bring these ideas to our blog, and in this post I’m taking the first step by setting the stage: on each page of today’s dilation challenges you’ll be asked to figure out which member of the dilation family is responsible for the function behavior you see and experience on the screen.

(Click the arrow at the bottom right of the sketch to go to the next challenge.)

We’ve put some of these activities on the web, with both the interactive sketch and the student directions on the same web page. You can try out the web version of the Dilation Function Family activity here.

[2022 Update] We now have an entire collection of online activities that focus on the connection  between geometric transformations and functions. Check it out!