Visualizing Exponential Functions with Base e

This GeoGebra example demonstrates how exponential functions with the natural base e behave visually, highlighting their characteristic growth/decay shape and how changes in the underlying parameter affect function values. The main mathematical concepts include the exponential function form (e.g., f(x)=a·e^x or related variants), key properties of functions over the real numbers, and the characteristic continuous curve behavior of exponential growth. Construction focuses on using several constructed point objects (A1, B1, C1, A2, A3, A4, A5, A6) as anchors to determine important locations and guide the resulting graph, so learners can compare values and read the curve’s structure directly. It is suitable for high school through early undergraduate audiences, especially for introducing exponential models before deeper calculus topics.