Reflecting the Exponential Function: y=e^x and y=ln(x) as Inverse Functions

① This GeoGebra applet demonstrates that reflecting the graph of y = e^x across the line y = x yields the graph of y = ln(x), visually illustrating the inverse relationship between exponential and logarithmic functions. ② Core mathematical concepts include exponential functions, logarithmic functions, inverse functions, reflection (mirror symmetry) across the line y = x, and the geometric interpretation of function inverses. ③ Construction details: using GeoGebra commands Point and Mirror, a point P is created on the exponential curve, and its reflection P' across the line y = x is generated; the functions f (y=e^x) and its reflected image are plotted, with text labels (text1, text2) showing the function expressions, allowing dynamic exploration as P moves along the curve. ④ Suitable for high school or early college students learning properties of exponential and logarithmic functions, inverse functions, and geometric transformations; also useful for classroom demonstrations to bridge algebraic and geometric understanding.