Transform Sine Horizontally, Stretch and Translate Together
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Sine and Cosine Functions
This example demonstrates how to horizontally transform a sine function and perform stretching and translation together. Key math concepts include function transformations, properties of the sine function, and geometric transformations. The construction uses GeoGebra commands like 'If', objects b (parameter), c (parameter), f (function object), text1 (text object), and A (point object). Suitable for high school students learning about function transformations to understand the rules of shifting and stretching function graphs.
GeoGebra Commands & Parameters
If(b > 0, (360 / ((4 * b)) + c, 1), If[b < 0, ((-3 * 360 / ((4 * b))) + c, 1), (0, 0)]) → A
AI Drawing Prompt Reference
Draw a sine function graph that demonstrates horizontal transformation, stretching, and translation together. Include a sine curve whose period and position are controlled by a parameter. Add a point on the graph whose location depends on the parameter's sign and magnitude: when the parameter is positive, the point sits at a specific peak; when negative, at another peak; when zero, at the origin. Show the curve's changing shape and the point's movement clearly, suitable for learning function transformation rules.
The prompt above was compiled from the original drawing commands and is for reference only.