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Mapping Diagram Composition Adjust Arrows

Mapping Diagram Composition Adjust Arrows
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2018-08-11 03:29
VectorFunctionGeometric Construction
This example demonstrates the composition of mapping diagrams and allows users to adjust arrows. Key mathematical concepts include functions and vectors. Using GeoGebra commands such as Point, Vector, and Sequence, users can visually understand the geometric meaning of function composition. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(y_{axis}) → P5
  2. Point(y_{axis}) → P9
  3. Point(y_{axis}) → P8
  4. Point(y_{axis}) → P7
  5. Point(y_{axis}) → P6
  6. Point(y_{axis}) → P4
  7. Point(y_{axis}) → P3
  8. Point(y_{axis}) → P2
  9. Point(y_{axis}) → P1
  10. SelectedElement(flist) → f
  11. Point(yAxis) → A
  12. If(d ≟ 1, y(A) - f(y(A)), 0) → align
  13. Vector(A, B) → u
  14. Textfield(f) → inputBox1
  15. Textfield(length) → inputBox4
  16. Sequence(t, t, y(A) + (n * Δx), y(A) - (n * Δx), (-Δx)) → t_*
  17. Zip((k, f(k)), k, t_*) → Graphfpts
  18. Zip((0, k), k, t_*) → SourcePtsMD
  19. Zip(f(k), k, t_*) → ft_*
  20. Zip((2, (y_{zoom} * (k + align))), k, ft_*) → fTargPts
  21. Zip(Vector[(0, k), (2, (y_{zoom} * (m + align)))], k, t_*, m, ft_*) → farr
  22. Vector(X_1, Y_1) → v
  23. Line(A, B) → h
  24. Intersect(f1, h, (2.7851193573624755E-10, -5.570238714724951E-10)) → C
  25. Zip(Vector[A, B], A, SourcePtsMD, B, fTGTpts) → fTGTarr
  26. Textfield(f1) → inputBox2
  27. SelectedElement(glist) → g
  28. Point(i) → Q5
  29. Point(i) → Q1
  30. Point(i) → Q2
  31. Point(i) → Q3
  32. Point(i) → Q4
  33. Point(i) → Q6
  34. Point(i) → Q7
  35. Point(i) → Q8
  36. Point(i) → Q9
  37. Zip((4, A), A, gft_*) → gTargPts
  38. Zip(Vector[A, B], A, fTargPts, B, gTargPts) → garr
  39. TableText(Transpose[{Join[{{"x"}, t_*}], Join[{{f}, ft_*}], Join[{{g}, gft_*}]}], "|_cc") → text13
  40. Zip(Vector[A, B], A, fTargPts, B, gTGTpts) → gTGTarr
  41. Textfield(g1) → InputBox1
  42. Zip((A, g(f(A))), A, t_*) → Graphgfpts

AI Drawing Prompt Reference

Draw a mapping diagram for function composition, showing arrows from a vertical axis on the left through a middle axis to a right axis. Place sample points on the left axis, connect them horizontally to the middle axis representing f(x), then draw arrows to the right axis for g(f(x)). Include editable text boxes for function inputs and draggable points to adjust arrow positions. Display a table with columns for x, f(x), and g(f(x)), and plot points of the composed function. The layout has three vertical axes with arrows flowing left-to-middle-to-right, illustrating the composition process.
The prompt above was compiled from the original drawing commands and is for reference only.