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Transforming the Graph of sin(x) to sin(x^2/4)

Transforming the Graph of sin(x) to sin(x^2/4)
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2020-10-23 05:05
FunctionTrigonometryTransformation
This example demonstrates how to transform the graph of sin(x) into sin(x^2/4). Key concepts include function graph transformation and trigonometry. Using GeoGebra commands like Sequence and CurveCartesian, the transformation process can be visually observed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(-6 + (0.1 * i), i, 0, 120) → X
  2. Sequence(i, i, -6, 6) → Z
  3. CurveCartesian(((1 - u) * t) + (u * t^(2) / 4), (k * f(t^(2) / 4)), t, -6, 6) → h

AI Drawing Prompt Reference

Draw a coordinate plane with x-axis from -6 to 6 and a suitable y-axis. First plot the basic sine curve. Then show its transformation: replace the variable with its square divided by four, resulting in a new curve that resembles the sine near the origin but stretches and changes period outward. Use a series of small dots or line segments to represent the transition from each point on the original sine curve to the corresponding point on the transformed curve, creating a dynamic visual mapping. The overall graph should clearly illustrate the geometric meaning of function transformation.
The prompt above was compiled from the original drawing commands and is for reference only.