I use this project in my classes to introduce the unit on function transformations in my algebra 2 classes. I've also used it as a review in my precalculus class. They are asked to study the most popular parent functions in several ways then use Desmos to explore what happens when they adjust the equations in various ways. This is a fairly open-ended exploration, and my students typically do a great job with that. I've included a basic rubric for grading purposes.

I have found that front-loading the transformations unit by having students explore them individually helps a great deal. Students who did a good job on this project did much better with the unit as a whole.

I typically follow up this project with one day of class giving summary notes, a graphic organizer, and some practice then another full day of student practice. There are some other fantastic resources on TPT for that :)