Visualization and Geometric Construction of Functions of Two Variables

①This example demonstrates the graphical representation of a function of two variables in 3D space, using GeoGebra's geometric construction tools to show the relationship between the function surface and related geometric elements. ②Core mathematical concepts include bivariate functions, 3D surfaces, parametric representation, and geometric transformations such as rotation and parallelogram construction, involving the interaction between function graphs and geometric objects. ③Construction highlights: from the construction summary, the Segment command is used to create segments, and objects f (function), A (point), a (parameter), and B (point) are defined, building a visualization framework for the function through these basic elements, possibly using sliders or parameters to control the function's shape. ④Suitable for high school to university-level mathematics teaching, for understanding multivariable calculus, spatial geometry, and dynamic mathematical exploration, as well as for intuitive demonstrations of optimization problems.