Dilation of Functions

This GeoGebra example demonstrates the dilation (scaling) transformation of function graphs, showing how a function is stretched or compressed along coordinate axes through geometric construction. The core mathematical concepts include function transformations, similarity transformations, scale factors, and the interplay between algebraic functions and geometric objects such as points, lines, and pyramids. The construction uses GeoGebra commands: Intersect, Dilate, Point, and Line, involving objects w, o_1, S, C, a, n, f, f_1, A, A', g, f_2, A'_1, and h. The Dilate command applies scaling to the function graph or related geometric elements, while Intersect identifies key points before and after transformation, enabling a visual comparison of the original and dilated functions. This resource is suitable for high school or early college students learning about function transformations and geometric transformations, and for teachers demonstrating dynamic mathematical principles in the classroom.