Domain-Range Swap: Quick Graphical Exploration

① This example dynamically illustrates the geometric meaning of swapping the domain and range of a function (i.e., the inverse function relationship), helping learners quickly grasp the symmetry between a function and its inverse about the line y=x. ② Core mathematical concepts include functions, inverse functions, domain, range, symmetry, and graph transformations, with connections to special points (like intersections) in calculus and function relations in differential equations. ③ Construction: Based on the summary, only one object f (a function) is used; GeoGebra commands define the function f and leverage its graph to demonstrate the symmetry, possibly with sliders or dynamic points for interactive exploration of the domain-range swap. ④ Suitable for high school to early college students, for teaching functions and inverse functions, visual understanding of symmetry, and as a supplementary tool in calculus for exploring function properties.