Geometric Visualization of an Exponential Function: Tangent and Mirror Construct

This example demonstrates key features of an exponential function using a geometry-first construction. It visualizes relationships among the curve, a tangent line, mirror (symmetry) operations, and intersection points to highlight how local and global behaviors can be connected visually. The core math concepts include exponential functions, tangency (the tangent line at a key point), geometric transformation via mirroring, and intersection-based determination of important points and constraints. Construction-wise, it is built with GeoGebra commands Point, Line, Intersect, Mirror, Tangent, and Segment. The construction includes function/curve objects such as f and g, a constraint or equation like eq1, and then derives multiple geometric points (e.g., A, B, C, C1, D, plus auxiliary points such as p, i, j, k and related objects like h and f1) to assemble the final diagram. Suitable for advanced high school through introductory university use, especially for lessons on graphing exponential functions, understanding tangency geometrically, and exploring transformation-based visual reasoning.