Teaching Trigonometric Transformations: Scaling, Shifting, and Intersections

This example demonstrates how to transform trigonometric functions and how the resulting graphs change in shape, position, and intersection points compared with the original function. The key mathematics concepts include trigonometry (sine/cosine/tangent graph properties), horizontal and vertical transformations (amplitude and period effects), phase shifts, and interpreting geometric features such as midlines/symmetry and intersection behavior. From the provided information, no GeoGebra construction commands are listed, so the construction workflow is best understood as: draw the baseline trigonometric function on the coordinate plane, apply transformation parameters in the function expression (e.g., coefficients and phase terms) to generate the transformed curve, and then compute or locate intersection points with the baseline (or reference lines) to discuss how transformations move and reshape the graph. Suitable for late secondary school through early pre-calculus/precalculus level, and useful for interactive classroom demonstrations and guided practice.