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变换顺序演示

变换顺序演示
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2019-03-06 00:27
函数解析几何最值优化函数图像
①本范例演示了在 GeoGebra 中通过不同顺序应用变换（如移动、缩放）对图形的影响；②涉及核心数学概念包括函数变换、解析几何、优化问题及二次函数；③作图要点提炼自构造摘要，使用了 If、FractionText、LaTeX、Sequence、Element、UnicodeToLetter、Corner、IndexOf、Defined、TableText、Polygon、Shuffle 等命令和对象；④适合高中及以上数学学习者，用于理解变换顺序对图形性质的影响及函数优化。

GeoGebra 命令及参数

  1. If(Random[0, 1] ≟ 1, (Random[1, 3] * 2) + 1, 1 / ((Random[1, 3] * 2) + 1)) → bVal
  2. FractionText(abs(bVal)) → bValDisp
  3. FractionText(abs(aVal)) → aValDisp
  4. LaTeX(case4) → case4Disp
  5. LaTeX(case3) → case3Disp
  6. LaTeX(case2) → case2Disp
  7. LaTeX(case1) → case1Disp
  8. Sequence((24, i), i, 22, 0, -2.75) → boxAnchorRight
  9. Element(B23:B28, caseIndx) → vStretchaVal
  10. Sequence((0, i), i, 22, 0, -2.75) → boxAnchorLeft
  11. Sequence({Element[boxAnchorLeft, i], Element[boxAnchorRight, i], Element[boxAnchorRight, i + 1], Element[boxAnchorLeft, i + 1]}, i, 1, 4) → boxAnchors
  12. Sequence(Polygon[Element[boxAnchors, i]], i, 1, 4) → boxes
  13. UnicodeToLetter(10007) → xmark
  14. UnicodeToLetter(10003) → cmark
  15. Corner(B10, 1) → C10
  16. Corner(B11, 1) → C11
  17. LaTeX((("\text{Vertical compression by a factor of \(" * FractionText[1 / abs(aVal)]) * "\).}")) → B12
  18. Corner(B12, 1) → C12
  19. LaTeX((("\text{Horizontal translation " * abs(cVal)) * " units right.}")) → B15
  20. Corner(B15, 1) → C15
  21. LaTeX((("\text{Horizontal translation " * abs(cVal)) * " units left.}")) → B16
  22. Corner(B16, 1) → C16
  23. Corner(B9, 1) → C9
  24. Element(boxes, 1) → box1
  25. Element(boxes, 2) → box2
  26. Element(boxes, 3) → box3
  27. Element(boxes, 4) → box4
  28. LaTeX((((("\text{Vertical translation " * abs(dVal)) * " unit") * If[abs(dVal) ≟ 1, "", "s"]) * " up.}")) → B18
  29. LaTeX((((("\text{Vertical translation " * abs(dVal)) * " unit") * If[abs(dVal) ≟ 1, "", "s"]) * " down.}")) → B17
  30. Corner(B17, 1) → C17
  31. Corner(B18, 1) → C18
  32. Element(caseFormulas, caseIndx) → fxLbl
  33. Sequence((((((("SetCoords(B" * Element[stepsChosen, i]) * ",x(Element(boxAnchorLeft,") * i) * ")),y(Element(boxAnchorLeft,") * i) * ")-.75))"), i, 1, Min[4, Length[stepsChosen]]) → cmdMoveSteps
  34. IndexOf(11, Remove[stepsChosen, {9, 10, 12, 13, 14, 15, 16}]) → F11
  35. IndexOf(9, Remove[stepsChosen, {10, 11, 12, 13, 14, 15, 16}]) → F9
  36. IndexOf(10, Remove[stepsChosen, {9, 11, 12, 15, 16}]) → F10
  37. IndexOf(12, Remove[stepsChosen, {9, 10, 11, 13, 14, 15, 16}]) → F12
  38. IndexOf(15, Reverse[Remove[stepsChosen, {9, 11, 12, 16, 17, 18}]]) → F15
  39. IndexOf(16, Reverse[Remove[stepsChosen, {9, 11, 12, 15, 17, 18}]]) → F16
  40. IndexOf(17, Reverse[Remove[stepsChosen, {13, 14, 15, 16, 18}]]) → F17
  41. IndexOf(18, Reverse[Remove[stepsChosen, {13, 14, 15, 16, 17}]]) → F18
  42. If(Defined[F9], F9 ≟ 1, true) → G9
  43. If(Defined[F10], F10 ≟ 1, true) → G10
  44. If(Defined[F11], F11 ≟ 1, true) → G11
  45. If(Defined[F12], F12 ≟ 1, true) → G12
  46. If(Defined[F15], F15 ≟ 1, true) → G15
  47. If(Defined[F16], F16 ≟ 1, true) → G16
  48. If(Defined[F17], F17 ≟ 1, true) → G17
  49. If(Defined[F18], F18 ≟ 1, true) → G18
  50. Defined(IndexOf[9, stepsChosen]) → I9
  51. Defined(IndexOf[10, stepsChosen]) → I10
  52. Defined(IndexOf[11, stepsChosen]) → I11
  53. Defined(IndexOf[12, stepsChosen]) → I12
  54. Defined(IndexOf[13, stepsChosen]) → I15
  55. Defined(IndexOf[14, stepsChosen]) → I16
  56. Defined(IndexOf[15, stepsChosen]) → I17
  57. Defined(IndexOf[16, stepsChosen]) → I18
  58. Sequence("\phantom{\dfrac{1}{1}000000000000000000000000000000000000000}", i, 1, 5) → spacers
  59. Sequence((-3, i), i, 9.5, 2.5, -2) → optionAnchors
  60. TableText({{"Step 1", "Step 2", "Step 3", "Step 4"}, spacers, markLst}, "vl") → stepLbls
  61. Polygon((-4, 0), (-4, 10), (44, 10), (44, 0)) → fbCover, fbCover_1, fbCover_2, fbCover_3, fbCover_4
  62. LaTeX(If[correctOrder, "Your solution is correct.", (((("The steps marked with " * moveUp) * " or ") * moveDown) * " are not in the correct order.")]) → fbCorrect
  63. LaTeX(If[correctOrder, "", "Click `Show a Solution' to see one correct solution."]) → fbShowSolution
  64. Shuffle(stepsCorrect) → stepsCorrectShuffled
  65. Sequence((((("SetValue(D" * Element[stepsCorrectShuffled, i]) * ",") * Element[optionAnchors, i]) * ")"), i, 1, Length[stepsCorrect]) → cmdSetHomePts
  66. LaTeX((((("\text{" * fbCorrect) * "\\") * fbShowSolution) * "}")) → fbStatement
  67. If(G10, correct, moveUp) → J10
  68. If(G9, correct, moveUp) → J9
  69. If(G11, correct, moveUp) → J11
  70. If(G12, correct, moveUp) → J12
  71. If(G15, correct, moveDown) → J15
  72. If(G16, correct, moveDown) → J16
  73. If(G17, correct, moveDown) → J17
  74. If(G18, correct, moveDown) → J18
  75. LaTeX((("\text{Horizontal compression by a factor of " * FractionText[abs(bVal)]) * ".}")) → B14
  76. LaTeX((("\text{Horizontal stretch by a factor of \(" * FractionText[1 / abs(bVal)]) * "\).}")) → B13
  77. Corner(B13, 1) → C13
  78. Corner(B14, 1) → C14
  79. IndexOf(14, Remove[stepsChosen, {9, 10, 11, 12, 13, 17, 18}]) → F14
  80. IndexOf(13, Remove[stepsChosen, {9, 10, 11, 12, 14, 17, 18}]) → F13
  81. If(Defined[F13], F13 ≟ 1, true) → G13
  82. If(Defined[F14], F14 ≟ 1, true) → G14
  83. Defined(IndexOf[17, stepsChosen]) → I13
  84. Defined(IndexOf[18, stepsChosen]) → I14
  85. If(G13, correct, moveUp) → J13
  86. If(G14, correct, moveUp) → J14
  87. LaTeX(If[isDone, ""]) → fbNotDone
  88. LaTeX((("\text{\textbf{Question: }A set of translations that would map \(f(x)=\vert x \vert\) onto \(h(x)=" * fxLbl) * "\) \\is listed below. Place the transformations in a correct order.}")) → MainInstruc
  89. LaTeX("\text{\textbf{Instructions: }Click on a transformation to select it. It will be placed in the list of steps in \\the order in which you select it. Click on a transformation already selected to return it to the \\list at the bottom.}") → SpecInstruc