Reflection Over a Graph

① This example demonstrates how to reflect a function graph over a given line (axis of symmetry) and dynamically observe the relationship between the original and reflected images. ② The core mathematical concept is reflection (axial symmetry) in plane geometry, involving function graphs, tangent lines, perpendicular lines, and loci, combined with algebraic expressions and interactive geometric construction. ③ Construction highlights: using GeoGebra commands such as Point, OrthogonalLine, Tangent, Intersect, Textfield, Mirror, Locus, and Segment, the construction includes function f, point A, perpendicular line h, tangent i, intersection j, reflected point A', locus loc1, as well as input boxes and buttons, allowing users to change the reflection axis or function parameters and update the reflected result in real time. ④ Suitable for high school or early college students learning geometric transformations and function graphs, and for teachers to demonstrate in class to help students intuitively understand the algebraic and geometric meaning of reflection.