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函数与其导数匹配

函数与其导数匹配
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2019-07-09 02:08
函数导数函数图像
①本范例演示如何将函数图像与其导数图像进行匹配；②涉及的核心数学概念包括函数、导数、图像识别；③作图要点——从下方『构造摘要』提炼用到了 Zip, Random, Flatten, NumberListToLatex, Shuffle, Polygon, Join, If, LaTeX, Translate, UnicodeToLetter, Sequence, Element, Derivative, Intersect 等GeoGebra命令/对象；④适合高中阶段学生学习微积分，理解函数与导数之间的关系。

GeoGebra 命令及参数

  1. Zip(Rotate[{Segment[(11, 0), (10.5, 0.5)], Segment[(11, 0), (10.5, -0.5)]}, A, (0, 0)], A, {0, 90°, 180°, 270°}) → TemplateAxisArrows
  2. Random(-5, 5) → t3var2
  3. Random(3, 10) → t3var1
  4. Flatten({Zip[x(A), A, {Intersect[t3Derivative1, 0, -10, t3var2]}], Zip[x(A), A, {Intersect[t3Derivative2, 0, t3var2Negative, 10]}]}) → t3zeros
  5. Random(-9, -5) → t22y1
  6. Random(t22y1 + 2, t22y1 + 5) → t22y3
  7. Random(t22y3 + 1, 9) → t22y4
  8. Random(t22y3 + 2, t22y3 + 4) → t22y2
  9. Random(t22x1 + 2, t22x1 + 5) → t22x2
  10. Random(t22x2 + 2, Min[8, 8 - t22x2]) → t22x3
  11. Random(-4, 4) → a2
  12. Zip(Derivative[A], A, t2Funcs) → t2Derivatives
  13. Zip(round(x(A), 1), A, {Intersect[Element[t2Derivatives, 1], 0, -11, 11]}) → t21zeros
  14. NumberListToLatex(t21zeros) → t21zerosTXT
  15. Random(1, 2) → t2Indx
  16. Random(a2 + 1, a2 + 4) → a3
  17. Random(-8, -2) → c2
  18. Random(c2 + 1, c2 + 3) → c3
  19. Random(c3 + 1, c3 + 3) → c4
  20. Random(c4 + 1, c4 + 3) → c5
  21. Random(-8, 0) → b2
  22. Random(b2 + 1, b2 + 4) → b3
  23. Random(b3 + 1, b3 + 4) → b4
  24. Shuffle({1, 2, 3}) → questionOrder
  25. Flatten(Sequence[Sequence[(i, j), i, -15, -15 + (2 * 24), 24], j, 10, 10 - 26, -26]) → transVectors
  26. Polygon({(-11, -11), (-11, 11), (11, 11), (11, -11)}) → polygonTemplate
  27. Shuffle({-1, 2, -2, 1}) → t1aVals
  28. Shuffle({2, 3, 4, 5, 6, -2, -3, -4, -5, -6}) → t1hVals
  29. Shuffle({2, 3, 4, 5, 6, -2, -3, -4, -5, -6}) → t1kVals
  30. Random(1, 4) → caseNum
  31. Join({Zip[Element[transVectors, A], A, questionOrder], Zip[Element[transVectors, B], B, matchOrder]}) → displayOrder
  32. If(Random[0, 1] ≟ 1, 1, -1) → a
  33. If(Random[0, 1] ≟ 1, 1, -1) → b
  34. LaTeX((((("\text{\textbf{Question: }" * QUESTION) * "\\\textbf{Instructions: }") * INSTRUCTIONS) * "}")) → allInstruc
  35. Translate(polygonTemplate, Vector[Element[displayOrder, 1]]) → graph1
  36. Translate(polygonTemplate, Vector[Element[displayOrder, 2]]) → graph2
  37. Translate(polygonTemplate, Vector[Element[displayOrder, 3]]) → graph3
  38. Translate(polygonTemplate, Vector[Element[displayOrder, 4]]) → graph4
  39. UnicodeToLetter(10003) → cmark
  40. UnicodeToLetter(10007) → xmark
  41. Translate(polygonTemplate, Vector[Element[displayOrder, 5]]) → graph5
  42. Translate(polygonTemplate, Vector[Element[displayOrder, 6]]) → graph6
  43. Shuffle({-2, -3, -4, -6}) → r1Vals
  44. Join({Sequence[Segment[(-11, i), (11, i)], i, -10, 10], Sequence[Segment[(i, -11), (i, 11)], i, -10, 10]}) → TemplateGrid
  45. Shuffle({1, 2, 3, 4, 5, 6}) → r2Vals
  46. Translate(polygonTemplate, Vector[Element[displayOrder, graphChosen]]) → highlightQuestion
  47. Sequence(i + 3 ≟ Element[matches, i], i, 1, 3) → correctMatches
  48. Translate(polygonTemplate, Element[displayOrder, 1]) → q1Box
  49. Translate(polygonTemplate, Element[displayOrder, 2]) → q2Box
  50. Translate(polygonTemplate, Element[displayOrder, 3]) → q3Box
  51. Translate(polygonTemplate, Element[displayOrder, Element[matches, 3]]) → q3MatchingBox
  52. Translate(polygonTemplate, Element[displayOrder, Element[matches, 2]]) → q2MatchingBox
  53. Translate(polygonTemplate, Element[displayOrder, Element[matches, 1]]) → q1MatchingBox
  54. Random(c2 + 1, c2 + 4) → d2
  55. Random(1, 3) → t1Indx
  56. Element(t2Funcs, t2Indx) → t2Func
  57. Derivative(t2Func) → t2Derivative
  58. Intersect(t3Base, (t3multiplier * 11), t3var2 + 0.1, 11) → t3RightBoundary
  59. Zip(Derivative[A], A, t1Funcs) → t1Derivatives
  60. Join({t1Funcs, t1Derivatives}) → t1AllFuncs
  61. Zip(Sort[{Intersect[A, polygonTemplate]}], A, t1AllFuncs) → t1endPoints
  62. Zip(If[x > x(Element[B, 1]) ∧ x < x(Element[B, 2]), C(x)], B, t1endPoints, C, t1AllFuncs) → t1FuncsRestricted
  63. Element(t1FuncsRestricted, t1Indx) → t1Func
  64. Element(t1FuncsRestricted, t1Indx + 3) → t1Derivative
  65. Random(1, 2) → t3Indx
  66. If(t3Indx ≟ 1, t3Restricted1, t3Restricted2) → t3Func
  67. If(t3Indx ≟ 1, t3Derivative1, t3Derivative2) → t3Derivative
  68. Zip(Translate[A, Vector[D]], A, {t1Func, t2Func, t3Func}, D, displayOrder) → funcSegmentsRow1
  69. Zip(Translate[A, Vector[D]], A, {t1Derivative, t2Derivative, t3Derivative}, D, Take[displayOrder, 4]) → funcSegmentsRow2
  70. Zip(Translate[TemplateGrid, Vector[A]], A, Take[transVectors, 1, 3]) → allGridsRow1
  71. Zip({Roots[A, -10, 10]}, A, t1Derivatives) → t1zeros
  72. LaTeX(If[Length[t21zeros] > 0 ∧ Defined[Element[t21zeros, 1]], fbt21WithZeros, fbt21NoZeros]) → fbt21
  73. If(t1Indx ≟ 1, fbt11, If[t1Indx ≟ 2, fbt12, fbt13]) → fbt1
  74. If(t2Indx ≟ 1, fbt21, fbt22) → fbt2
  75. If(t3Indx ≟ 1, fbt31, fbt32) → fbt3
  76. Translate(Flatten[Zip[{(x(A), Slope[Line[A, B]]), (x(B), Slope[Line[A, B]])}, A, t22Points, B, Take[t22Points, 2]]], Element[displayOrder, 5]) → t22DerivativeEndPoints
  77. Join({TemplateAxisArrows, {Zip[Segment[(A, -0.3), (A, 0.3)], A, {-10, -5, 5, 10}], Zip[Segment[(0.3, B), (-0.3, B)], B, {10, 5, -5, -10}], {Segment[(-11, 0), (11, 0)], Segment[(0, -11), (0, 11)]}}}) → TemplateAxis
  78. Zip(Translate[TemplateGrid, Vector[A]], A, Take[transVectors, 4, 6]) → allGridsRow2
  79. Zip(Translate[TemplateAxis, Vector[A]], A, Take[transVectors, 1, 3]) → allAxesRow1
  80. Zip(Translate[TemplateAxis, Vector[A]], A, Take[transVectors, 4, 6]) → allAxesRow2
  81. Zip(Zip[Text[A, B + V, true, true], A, {"-10", "-5", "5", "10", "x", "-10", "-5", "5", "10", "y"}, B, TemplateTxtLocations], V, Take[transVectors, 4, 6]) → allAxisLabelsRow2
  82. Zip(Zip[Text[A, B + V, true, true], A, {"-10", "-5", "5", "10", "x", "-10", "-5", "5", "10", "y"}, B, TemplateTxtLocations], V, Take[transVectors, 1, 3]) → allAxisLabelsRow1
  83. Zip(Text[A, (2, 14.5) + V, true, true], A, graphTitles, V, transVectors) → allTitles
  84. LaTeX(("\text{\textbf{Feedback: } (A checkmark in a column indicates a correct match.)\\" * If[IndexOf[fbIndx, questionOrder] ≟ 1, fbt1, If[IndexOf[fbIndx, questionOrder] ≟ 2, fbt2, fbt3]])) → fbDisplay
  85. Zip(Text[If[A, "", ("" * xmark)], V + (7.5, 14.2), true, true], A, correctMatches, V, displayOrder) → xMarks
  86. Zip(Text[If[A, ("" * cmark)], V + (7.5, 14.2), true, true], A, correctMatches, V, displayOrder) → checkMarks

AI 绘图提示语参考

绘制一个包含多个函数图像及其导数的图形，展示函数与其导数的关系。首先创建一个坐标轴，然后在坐标轴上随机生成几个函数和它们的导数，并标出函数和导数的零点。将这些函数和导数的图像以及零点信息组合在一起，形成一个匹配游戏，让用户识别哪些图像属于同一函数及其导数。最后，将所有这些元素排列在一个网格中，突出显示其中一个函数及其导数，以便用户进行比较和匹配。
以上提示语为根据原始绘图命令整理而来，仅供参考。