Understands and applies rate of change
A key concept in the study of functions is rate of change. Rate of change is the rate at which one variable changes with respect to another. Situations involving rate of change include the speed of a car, the number of people per year by which a population increases, and slope of a line.
Rate of change should be analyzed in multiple ways including: numeric, symbolic (recursive and explicit), and graphic representations. Students should approximate and interpret rate of change based on graphs, numerical data, and real world situations. The study of rate of change focuses on slope and lays the groundwork for calculus. Students should distinguish between a constant rate of change and a non-constant rate of change or a constant proportional rate of change (exponential change). In addition, students should investigate finite differences (e.g., the rate of change of the rate of change).