Algebraic Expressions for Function Transformations

This example demonstrates how to express function transformations algebraically—such as shifts, reflections, and vertical/horizontal scalings—and then verify the results by comparing the corresponding graphs in GeoGebra. The key ideas include writing transformed functions via algebraic substitution in the input (x) and algebraic modification of the output (f(x)), and interpreting how coefficients affect direction, scale, and displacement on the graph. Construction-wise, even though no specific GeoGebra “construction summary/commands” were provided, the workflow is typically: (1) define a base/reference function, (2) build the transformed function using the corresponding algebraic rules, (3) plot both graphs in the same coordinate plane, and (4) use visual comparison (optionally marking key points) to confirm the transformation’s effect. Suitable for secondary-level and early undergraduate learners, especially for lessons on functions, graphing, and algebraic modeling of transformations.