MHF4UC Transformations of Exponential Functions

① This GeoGebra example dynamically demonstrates transformations of exponential functions of the form y = a·f(k(x-d)) + c, showing how translations, stretches, and reflections affect the graph. ② Core mathematical concepts include exponential functions, function transformations (horizontal/vertical shifts, horizontal/vertical scaling, reflections across axes), and the geometric meaning of parameters k, a, d, and c. ③ Construction highlights: from the summary, sliders k, a, d, c control transformation parameters; functions f and g define the original and transformed functions; parent and trans represent the parent function and the transformed result; standard and subbed handle expression standardization and substitution; origlabel and translabel label the graphs. The construction creates an interactive environment for exploring transformations. ④ Suitable for high school (e.g., MHF4UC course) or pre-university students learning function transformations, and for teachers to demonstrate how parameter changes correspond to graph shifts, stretches, and compressions.