Exponential Functions: Dynamic Exploration of Parameter Effects

This example demonstrates how the graph of an exponential function changes as parameters vary, using sliders to adjust base, coefficient, and horizontal shift. It visually illustrates the fundamental shape, monotonicity, and asymptote behavior of exponential functions, along with geometric transformations such as translation and scaling. The construction uses GeoGebra sliders for parameters k, b, a, and h, and defines the function f, allowing real-time observation of graph changes. Core concepts include exponential growth/decay, transformations, and function equations. Suitable for high school and early college students learning exponential functions, as well as for classroom demonstrations or self-study to build intuition about parameter-graph relationships.