GeoGebra Visualization of Inverse Functions via Symmetry

This GeoGebra example demonstrates inverse functions by showing how a function’s graph transforms into the inverse graph. The key idea is the geometric correspondence under symmetry about the line y = x: if a point (x, y) lies on the graph of f, then (y, x) lies on the graph of f^{-1}. It focuses on core concepts including functions, inverse functions, and the visual criterion for being mutually inverse through coordinate swapping. Construction uses many coordinate-labeled point objects (e.g., A1, A2, B1, C1, …, Z1, AA1, plus additional points like O and P1) to mark key (x, y) and swapped (y, x) positions that define the relationship between the original and inverse graphs. The setup may also organize the display using polygonal or trapezoid-like boundary structures to emphasize shape and correspondence. Suitable for upper secondary to early university learners, especially for teaching function graphs, transformations, and inverse relationships.