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Function Graph Transformations Demo

Function Graph Transformations Demo
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2020-11-27 14:39
FunctionCoordinate GeometryGeometric ConstructionGraphing
In collections Grade 12 PreCalculus BC
This example demonstrates the geometric process of transforming function graphs through point manipulation. It involves core math concepts like function graph translation, equilateral triangle construction, and coordinate geometry. Key GeoGebra commands and objects used include If, Random, RandomElement, Max, Min, Corner, and objects like f1, f3, f2, fn, f, A, yaa, xaa, qQ, c, cC, absc, xc, blist, b, bB, xa, B, C, alist, a, aA, d, dD, g, xbim, xaim, AANS, BANS, xcim, CANS, ymax, ymin1, B', C', vscale, ymin2, e, atext, ctext. Suitable for high school mathematics teaching to understand function graph transformation rules and programming applications.

GeoGebra Commands & Parameters

  1. If(fn ≟ 1, f1, If[fn ≟ 2, f2, f3]) → f
  2. If(fn ≤ 2, (-2, f(-2)), (-4, f(-4))) → A
  3. Random(-8, 8) → c
  4. If(qQ ≟ 2 ∨ qQ ≟ 3 ∨ qQ ≟ 4, 0, c) → cC
  5. If(fn ≟ 3, 4, 2) → xc
  6. RandomElement(blist) → b
  7. If(qQ ≟ 1 ∨ qQ ≟ 2 ∨ qQ ≟ 5, 1, b) → bB
  8. If(fn ≟ 3, -4, -2) → xa
  9. If(fn ≤ 2, (2, f(2)), (4, f(4))) → C
  10. RandomElement(alist) → a
  11. If(qQ ≟ 1 ∨ qQ ≟ 3, 1, a) → aA
  12. Random(-10, 10) → d
  13. If(qQ ≟ 4, 0, d) → dD
  14. If(bB > 0, xa / abs(bB) + cC, ((-xa)) / abs(bB) + cC) → xaim
  15. If(bB > 0, xc / abs(bB) + cC, ((-xc)) / abs(bB) + cC) → xcim
  16. Max({8, y(AANS) + 2, y(BANS) + 2, y(CANS) + 2}) → ymax
  17. Min({-5.8, y(AANS) - 1.8, y(BANS) - 1.8, y(CANS) - 1.8}) → ymin1
  18. If(aA ≟ 1, "", If[aA ≟ -1, "-", Text[aA]]) → atext
  19. If(cC ≟ 0, "", If[cC < 0, ("+" * Text[absc]), ("-" * Text[absc])]) → ctext
  20. If(bB ≟ 1, "", If[bB ≟ -1, "-", Text[bB]]) → btext
  21. If(dD ≟ 0, "", If[dD > 0, ("+" * Text[dD]), Text[dD]]) → dtext
  22. If(qQ ≟ 1, q1text1, If[qQ ≟ 2, q2text2, If[qQ ≟ 3, q3text3, If[qQ ≟ 4, q4text4, If[qQ ≟ 5, q5text5, q6text6]]]]) → qftext
  23. Corner(5) → dims
  24. Max({4 / abs(bB) + cC + 2, 8}) → xmax
  25. Min({-4 / abs(bB) + cC - 2, -8}) → xmin

AI Drawing Prompt Reference

Draw a function graph transformation demonstration with three basic functions f1, f2, and f3. Show function graph translations and scalings through point coordinates A, C, and B. First, randomly select a function, then demonstrate function graph translations through point A and C coordinates, and show function graph scalings through point B coordinates. Finally, adjust the y-axis limits to ensure the graph is clearly visible.
The prompt above was compiled from the original drawing commands and is for reference only.