Line Reflections of Functions: Dynamic Geometry Demo

①This GeoGebra example dynamically demonstrates the reflection of function graphs across arbitrary lines, showing the relationship between the original and reflected functions. ②Core mathematical concepts include reflection (axial symmetry), function graph transformations, line equations, and various function types such as trigonometric, quadratic, and normal distribution curves. ③Construction uses commands: OrthogonalLine to create perpendiculars, Line for the reflection axis, Mirror to perform reflection, Intersect to find intersection points, Point to mark key points, Segment to connect segments, and Angle to measure angles; objects include multiple functions f, f_1 to f_4, and points A, B with their reflected images A', A'', etc., with sliders or parameters controlling the axis position. ④Suitable for high school and above to study function transformations, coordinate geometry, and geometric construction, also useful for university basic math courses or teacher demonstrations to visualize the geometric essence of reflection.