Rotating a Function: Dynamic Coordinate Transformation

①This example demonstrates how to rotate a function curve around the origin by an arbitrary angle, visually showing the resulting image transformation. ②The core mathematical concept is the rotation transformation in coordinate geometry, involving rigid motion of the function graph and the coordinate mapping between original and rotated points. ③Construction highlights: using the GeoGebra Rotate command with the function f as the object, angle α as the rotation parameter, generating the rotated image f_1; a slider controls α for dynamic observation. ④Suitable for high school or early college students to understand function graph transformations, coordinate rotation in analytic geometry, and to build intuition for later topics like differential equations or similarity transformations.