Exponential–Logarithmic Inverse Mapping with Slope/ Difference Visualization

This GeoGebra example demonstrates the inverse relationship between exponential and logarithmic functions by constructing corresponding geometric features and highlighting how values change locally. It centers on key ideas such as exponential/logarithmic functions as mutual inverses, the “difference and slope” viewpoint for understanding how a function varies near a point, and slope-related intuition that supports later study in calculus. Construction highlights include using Invert to create inverse (corresponding) mappings, LaTeX to label derived expressions (text1/text2/text3), Point to place key reference points (a, a_1, A, b, B, C), Intersect to compute intersection points that form the visual relationships, and OrthogonalLine to draw perpendicular lines used in the geometric slope/direction interpretation. Suitable for secondary advanced students and early university learners, especially for graphing, inverse functions, and pre-calculus intuition before formal derivatives.