Function or Not? Dynamically Visualizing Functions, Riemann Sums, and Limits

This example dynamically illustrates what makes a relation behave like a function by showing how function graphs are built and checked through plotted geometric components. It also visualizes upper and lower sums (Riemann-sum style) so that students can observe how the approximating quantities evolve and converge as the partition becomes finer, highlighting the limit process. Key concepts include function graphs, upper/lower sum interpretation of area-like quantities, convergence toward a limiting value, and (optionally) the role of exponential-type behavior reflected by the included parameters. Construction-wise, it uses GeoGebra commands such as Point to place key vertices (A, B, C and their primed/shifted variants), Vector together with Dilate to create and scale the geometric segments that represent each sub-interval’s contribution, and Textfield/Text plus interactive controls (button and input box objects) to label relationships and drive the dynamic behavior. Suitable for high school advanced topics through early calculus courses and for classroom demonstrations on graph-based reasoning, Riemann sums, and limits.