Graph Transformations: Enlargement and Reflection
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This GeoGebra example demonstrates function graph transformations, specifically enlargement (scaling) and reflection across axes. It visually shows how a function's graph changes under scaling factors and mirroring, illustrating the effects of parameter modifications on the graph's shape and position. The construction utilizes defined functions and geometric objects to model the transformed graphs, allowing interactive exploration of transformation rules. It is suitable for middle to high school mathematics, particularly in algebra and function units, and serves as an effective tool for teaching and learning graph transformation concepts.
GeoGebra Commands & Parameters
h(x) = (((x - 2) * (x - 3)) * (x + 1)) - 2f(x) = (0.3 * h(x))Numeric p(1)Numeric q(1)g(x) = (q * f((p * x)))
AI Drawing Prompt Reference
Draw a graph showing transformations of a cubic function. Start with a cubic curve that crosses the x-axis near -1, 2, and 3, and is shifted down by 2 units. Then show a vertically compressed version of this curve, scaled by a factor of 0.3, making it flatter. Finally, apply a horizontal scaling by parameter p (initially 1) and a vertical scaling by parameter q (initially 1) to get the final transformed curve. Display all three curves in different colors or line styles, with labeled axes.
The prompt above was compiled from the original drawing commands and is for reference only.