Graph Transformation for k·f(x): Piecewise and Tangent-Style Insight

This GeoGebra example demonstrates how multiplying a function f(x) by a constant k transforms the graph into k·f(x), highlighting the correspondence between the original and transformed curves on the same coordinate plane. It emphasizes key ideas in function transformation—specifically vertical scaling (stretching or compressing in the y-direction)—and uses piecewise-function structure to reflect rule changes across intervals. The original topic tags also indicate a tangent/tangency viewpoint tied to trigonometric thinking, providing geometric intuition for local behavior such as slope or tangent-like constructions. Construction-wise, the model relies on GeoGebra geometry tools such as Point and Segment to build essential objects: the parameter k, the function f, characteristic points (A, B, C), and additional control/anchor points (e, a), together with points T1, T3, T4 that capture the alignment of notable features before and after transformation. The resulting setup is well suited for secondary school instruction on function graphs and transformations, and for introductory pre-calculus / early calculus lessons where students learn to interpret piecewise graphs via visual reasoning.