Transforming Exponential Functions: Translations, Dilations, and Reflections

This GeoGebra example demonstrates how exponential functions are transformed through translations, dilations (stretches and compressions), and reflections in the Cartesian coordinate system, visually showing how parameter changes affect the graph’s shape, position, and orientation. Core mathematical concepts include exponential functions, function transformations, graph translation, vertical and horizontal dilation, reflection across axes, and symmetry in the coordinate plane. Construction highlights: The example applies GeoGebra commands Root, Extremum, Mirror, Roots, and Intersect to construct key points, extrema, roots, and intersection points. Objects involved include p, n, c, b, a, A, D, text5, i, v, text1, d, e2, f, v_1, g, v_2, h, B, C, E, text2, text3, t, s, r, w, e, v_3, j, enabling dynamic generation of transformed exponential curves and auxiliary annotations. Suitable for high school mathematics instruction on functions and elementary functions, classroom demonstrations, and independent student exploration of exponential graph transformation rules.