Practice: Inverse Function Graph Symmetry

This GeoGebra example demonstrates the key graphical relationship between a function and its inverse: the inverse function’s graph is obtained by reflecting the original graph across the line y = x. The core concepts include inverse functions, the meaning of function-image correspondence, and the geometric intuition behind features such as tangency behavior (including understanding how a tangent-type function’s characteristic shape is mirrored in the inverse). Construction focuses on interactive labeling and setup: it uses Textfield to create and position text labels (text1, text2, text3, label) and employs an InputBox2 so users can enter or adjust relevant inputs/parameters for the displayed functions. A rotated label (\rotatebox{90}{label}) is used to improve readability of annotations. Suitable for late secondary school through early college, for lessons and practice on inverse functions, graph transformations, and function interpretation via visual geometry.