Try It: Writing Logarithmic Functions from Graph Clues

This interactive example guides students to write down a logarithmic function and match it to the displayed curve, building intuition about how parameters control the graph. It focuses on logarithmic functions such as y=log_a(x) and the transformed form y=log_a(x-h)+k, emphasizing how the base and vertical/horizontal shifts determine the curve’s features (including the asymptotic behavior and key intercepts). Construction relies on GeoGebra commands and structures reflected in the build: Intersect to locate crucial points from geometry/coordinates, Vector to encode displacement or directional information, Random and RandomElement to generate practice variations, and Textfield/InputBox1 to show or accept function expressions and prompts. The listed objects (including points/expressions like g, h, k1, A, G, u, k, l, m, n, o, q, eq2, M, N, r) together with button1 manage the exercise state and updates, enabling a “graph-to-formula” workflow. Suitable for upper secondary and early college courses on functions and logarithms, as well as classroom drills and self-paced practice.