Finding Average Rate of Change from Graphs (GeoGebra Practice)

This example demonstrates how to determine the average rate of change of a function between two points by using the graph and its secant line. It centers on the geometric interpretation of the average rate as the slope of the secant (the rise-over-run between two selected points). Key concepts include average rate of change, secant slope, function graphs, and the difference quotient formed from coordinate differences. The construction approach is: plot the function curve in a coordinate plane, choose two x-values (or two points) on the graph, create the secant line connecting them, and compute the average rate from the two points’ coordinates (using subtraction to form Δy and Δx). Although no explicit GeoGebra command list is provided in the source “construction summary,” the essential objects are the function graph, the two points on the curve, the line through the points (secant), and the calculation of slope/average rate from the coordinates. Suitable for advanced high school through the beginning of college calculus courses, especially for building intuitive understanding before or alongside derivative topics.