Rates of Change and Growth/Decay Characterization

This activity provides students with an opportunity to practice calculating rates of change and then to connect the patterns they see in these calculations to the growth/decay they see in the graph. This allows us to characterize linear functions as having a constant rate of change and to see that concave up functions have increasing rates of change and concave down functions have decreasing rates of change.

This is a slightly updated version of this activity https://sites.google.com/site/ruinstructorprecalcwiki/chapter-1-activities/course-activity-1-3-linear-functions and more implementation notes are provided there.

I have created the following Desmos activity to use in class after students have worked on this activity. The activity itself could definitely be assigned as out of class work and then you could follow up in class with the Desmos activity.

https://teacher.desmos.com/activitybuilder/custom/59a580a4ffa2d2777a043799