Visualizing Function Transformations af(b(x-c))+d

This GeoGebra example features three interactive applets that systematically demonstrate the complete transformation of a function y = af(b(x-c))+d, covering vertical scaling, horizontal scaling, horizontal shift, and vertical shift. The core mathematical concept is affine transformations of function graphs, including amplitude changes, period changes, and the effect of translations on graph position. The construction uses GeoGebra's If command and slider objects (such as a, b, c, d) to dynamically control parameters, along with auxiliary functions and text labels (like atext, dtext) to display the transformation formula in real time. Suitable for high school and above in the unit of function transformations, this resource serves as an interactive tool for classroom demonstrations or student self-exploration, helping learners intuitively grasp how parameter changes jointly affect the shape and position of function graphs.