Multiplicative 5.1: Piecewise Functions and Sphere under Similarity

①This example demonstrates how a multiplicative factor drives similarity transformations in 3D space, affecting the shapes of piecewise functions and a sphere. ②Core mathematical concepts include linear programming/optimization, piecewise functions, similarity transformations, spheres, and curve sketching, bridging algebra and geometry. ③Construction highlights: although no explicit GeoGebra commands are listed, the tags suggest the use of sliders to control the multiplicative factor, function objects for piecewise definitions, sphere objects, similarity transformation tools, and curve sketching to visualize the transformed shapes. ④Suitable for high school to undergraduate mathematics, particularly for teaching geometric transformations, function graphing, and optimization problems, offering an interactive way to explore how scaling alters graphical structures.