GeoGebra Practice: Piecewise Functions via Geometric Construction

This example demonstrates how a piecewise function can be visualized by defining different rules on different intervals and then “stitching” the corresponding pieces together into a single graph. It focuses on the graphical phenomenon of how function definitions change across boundaries, and how that change determines the shape and junction behavior of the overall curve. The key math concepts include piecewise functions, function graphing on separate domains, and the use of supporting geometry ideas such as ratios and similarity (to locate critical points and guide segment slopes or segment transitions). Construction-wise, the GeoGebra workflow is driven by the main objects listed in the construction summary (A1–A7): these represent the critical points/auxiliary geometric entities used to compute and constrain the piecewise components, ensuring the correct interval endpoints and the resulting connected graph. Suitable for high school through early college, especially for classroom practice and for students learning to connect algebraic definitions of piecewise functions to their visual graph forms.