Sine Function Transformations by Ann DeFranco
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This example demonstrates transformations of the sine function, including translations and scalings. It involves core math concepts like the sine function, function transformations, and parameter effects. GeoGebra commands used include Function, If, with objects like vamp, hamp, hs, vs, text elements, and function definitions. Suitable for high school mathematics education to understand function graph transformation rules.
GeoGebra Commands & Parameters
Function(sin(x), 0, 6.28) → fIf(b ≟ true, -1, 1) → xrflIf(a ≟ true, -1, 1) → yrflFunction(((xrfl * vamp) * sin(((yrfl * hamp) * x) - hs)) + vs, Min[((yrfl * 1 / hamp) * (0 + hs)), ((yrfl * 1 / hamp) * (hs + 6.28))], Max[((yrfl * 1 / hamp) * (hs + 6.28)), ((yrfl * 1 / hamp) * (0 + hs))]) → h
AI Drawing Prompt Reference
Draw a sine function graph and demonstrate its translations and scalings. Start by plotting the basic sine curve, then reflect it along the x-axis and y-axis based on parameters. Next, apply transformations like scaling and translation to the sine curve using parameters, and finally label key parameters and transformation effects on the graph to illustrate the rules of function graph transformations.
The prompt above was compiled from the original drawing commands and is for reference only.