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Function Composition: Dynamic Illustration

Function Composition: Dynamic Illustration
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2016-12-28 03:32
FunctionTransformationSlider AnimationGraphing
This example demonstrates the concept of function composition through a dynamic and modifiable illustration. Key mathematical concepts include functions, function composition, and dynamic modification. It uses commands such as Intersect, Textfield, Dilate, Segment, Vector, Translate, and Rotate in GeoGebra. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(f, r) → P
  2. Textfield(a) → InputBox1
  3. Textfield(f) → InputBox2
  4. Textfield(g) → InputBox3
  5. Intersect(g, h, 1) → E
  6. Dilate(F, If[0 < d ≤ 1, 1 - d, 0], A) → F'
  7. Segment(F, F') → i
  8. Dilate(A, If[1 < d ≤ 2, 2 - d, 0], B) → A'
  9. Segment(A, A') → j
  10. Dilate(B, If[2 < d ≤ 3, 3 - d, 0], G) → B'
  11. Vector(B, B') → u
  12. Translate(A, u) → A'_1
  13. Translate(A', u) → A''
  14. Segment(A'_1, A'') → j'
  15. Rotate(A'_1, If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → H
  16. Rotate(A'', If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → A'''
  17. Segment(H, A''') → j''
  18. Rotate(A'_1, If[3 < d ≤ 4, ((d - 3) * π / 2), π / 2], F) → I
  19. Rotate(A'', If[3 < d ≤ 4, ((d - 3) * π / 2), π / 2], F) → A'''_1
  20. Dilate(D, If[4 < d ≤ 5, 5 - d, 0], E) → D'
  21. Segment(D, D') → l
  22. Dilate(A, If[1 < d ≤ 2, 2 - d, 0], C) → A'_2
  23. Segment(A, A'_2) → m
  24. Dilate(C, If[2 < d ≤ 3, 3 - d, 0], J) → C'
  25. Vector(C, C') → v
  26. Translate(A, v) → A'_3
  27. Translate(A'_2, v) → K
  28. Segment(A'_3, K) → m'
  29. Rotate(A'_3, If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → L
  30. Rotate(K, If[3 < d ≤ 4, ((-(d - 3)) * π / 2), ((-π)) / 2], F) → K'
  31. Segment(L, K') → m''
  32. Intersect(g, p, 1) → N
  33. Dilate(O, If[4 < d ≤ 5, 5 - d, 0], P) → M'
  34. Segment(M, M') → q