Reasoning About Exponential Graphs (Part 1): Growth, Decay, and Key Features

This example demonstrates how to reason from exponential function graphs to infer qualitative behavior such as growth vs. decay and to identify key visual features. The core mathematical ideas include the standard form of an exponential function, the effect of the base on the curve’s shape, the horizontal asymptote behavior, intercepts (especially at x=0), and graph-based strategies for algebraic reasoning. The provided GeoGebra command “construction summary” is empty, so the exact command list cannot be reconstructed; however, the intended construction is consistent with using a function/graphing workflow in GeoGebra to plot an exponential curve and then analyze how parameter choices change the graph. Suitable for upper secondary to early university students, and for lessons on function understanding, graph–algebra connections, and guided exploration.