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Function Transformations Demo

Function Transformations Demo
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2020-12-17 23:55
FunctionTrigonometryTransformation
This example demonstrates three transformations of the function k*f(bx)+a. It covers core math concepts like function transformations and the impact of parameters (k, b, a). Constructed using GeoGebra commands Max, Vector, Distance, Segment with objects like g, f, a, h_1, b, h_2, k, h_3, A, B, u, etc. Suitable for high school mathematics teaching to understand function graph transformation rules.

GeoGebra Commands & Parameters

  1. Max(f, -5, 5) → A
  2. Max(h_1, -5, 5) → B
  3. Vector(A, B) → u
  4. Distance(B, A) → afstandBA
  5. Vector(A, C) → w
  6. Distance(A, C) → afstandAC
  7. Segment(A, E) → h
  8. Segment(D, A) → i

AI Drawing Prompt Reference

Create a plane diagram that illustrates function parameter transformations using key geometric constructions. First, consider two function graphs (the original and two transformed/related reference functions) and, within the same horizontal range, determine their maximum points, placing them as points A and B. Draw the vector from A to B and indicate the distance between B and A. Determine another point C as the corresponding reference point associated with the chosen second curve, and add the distance from A to C. Finally, draw segments from A to E (segment h) and from D to A (segment i) so the vectors and distance relationships reflect the effect of the parameters in the transformation.
The prompt above was compiled from the original drawing commands and is for reference only.