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用方程表示表格数据 by Matthew Zeigler (3)

用方程表示表格数据 by Matthew Zeigler (3)
几何画板及绘图内容加载中，请稍等……
2015-02-06 01:22
函数数列解析几何函数图像
本范例演示如何通过 GeoGebra 将表格数据转化为线性函数方程。涉及的核心数学概念包括方程表示、除法、线性函数。作图要点包括使用 Sequence, Sort, Random, Element, Join, FractionText, If, TableText 等命令，以及 button1, list2, list1, coefs, A1, startingX1, A2, intervalX1, A3, A4, A5, A6, coef1, A7, coef2, coef3, coef4, coef5, b2, b3, b4, b5, coef6, b, b6, b1, B2, B3, B4, B5, B6, B7, D1, startingX2, D2, intervalX2, D3, D4, D5, D6 等对象。适合初中及以上学生用于理解数据与函数的关系，以及掌握方程构建技巧。

GeoGebra 命令及参数

  1. Sequence(i, i, 1, 20) → list2
  2. Sequence((-i), i, 1, 20) → list1
  3. Sort(Join[{list1, list2}]) → coefs
  4. Random(0, 20) → startingX1
  5. Random(0, 10) → intervalX1
  6. Element(coefs, Random[1, 20]) → coef1
  7. Element(coefs, Random[1, 20]) → coef2
  8. Element(coefs, Random[1, 20]) → coef3
  9. Element(coefs, Random[1, 20]) → coef4
  10. Element(coefs, Random[1, 20]) → coef5
  11. Element(coefs, Random[1, 20]) → coef6
  12. Join({list1, list2, {0}}) → b
  13. FractionText((coef1 * A2^(2)) + b1) → B2
  14. FractionText((coef1 * A3^(2)) + b1) → B3
  15. FractionText((coef1 * A4^(2)) + b1) → B4
  16. FractionText((coef1 * A5^(2)) + b1) → B5
  17. FractionText((coef1 * A6^(2)) + b1) → B6
  18. FractionText((coef1 * A7^(2)) + b1) → B7
  19. Random(0, 20) → startingX2
  20. Random(0, 10) → intervalX2
  21. FractionText((coef2 * D2^(2)) + b2) → E2
  22. FractionText((coef2 * D3^(2)) + b2) → E3
  23. FractionText((coef2 * D4^(2)) + b2) → E4
  24. FractionText((coef2 * D5^(2)) + b2) → E5
  25. FractionText((coef2 * D6^(2)) + b2) → E6
  26. FractionText((coef2 * D7^(2)) + b2) → E7
  27. Random(0, 20) → startingX3
  28. Random(0, 10) → intervalX3
  29. FractionText((coef3 * G2^(2)) + b3) → H2
  30. FractionText((coef3 * G3^(2)) + b3) → H3
  31. FractionText((coef3 * G4^(2)) + b3) → H4
  32. FractionText((coef3 * G5^(2)) + b3) → H5
  33. FractionText((coef3 * G6^(2)) + b3) → H6
  34. FractionText((coef3 * G7^(2)) + b3) → H7
  35. Random(0, 20) → startingX4
  36. Random(0, 10) → intervalX4
  37. FractionText((coef4 * J2^(2)) + b4) → K2
  38. FractionText((coef4 * J3^(2)) + b4) → K3
  39. FractionText((coef4 * J4^(2)) + b4) → K4
  40. FractionText((coef4 * J5^(2)) + b4) → K5
  41. FractionText((coef4 * J6^(2)) + b4) → K6
  42. FractionText((coef4 * J7^(2)) + b4) → K7
  43. Random(0, 20) → startingX5
  44. Random(0, 10) → intervalX5
  45. FractionText((coef5 * M2^(2)) + b5) → N2
  46. FractionText((coef5 * M3^(2)) + b5) → N3
  47. FractionText((coef5 * M4^(2)) + b5) → N4
  48. FractionText((coef5 * M5^(2)) + b5) → N5
  49. FractionText((coef5 * M6^(2)) + b5) → N6
  50. FractionText((coef5 * M7^(2)) + b5) → N7
  51. Random(0, 20) → startingX6
  52. Random(0, 10) → intervalX6
  53. FractionText((coef6 * P2^(2)) + b6) → Q2
  54. FractionText((coef6 * P3^(2)) + b6) → Q3
  55. FractionText((coef6 * P4^(2)) + b6) → Q4
  56. FractionText((coef6 * P5^(2)) + b6) → Q5
  57. FractionText((coef6 * P6^(2)) + b6) → Q6
  58. FractionText((coef6 * P7^(2)) + b6) → Q7
  59. If(b1 < 0, (-b1), b1) → forTextb1
  60. If(b2 < 0, (-b2), b2) → forTextb2
  61. If(b3 < 0, (-b3), b3) → forTextb3
  62. If(b4 < 0, (-b4), b4) → forTextb4
  63. If(b5 < 0, (-b5), b5) → forTextb5
  64. If(b6 < 0, (-b6), b6) → forTextb6
  65. If(b1 < 0, " - ", " + ") → sign1
  66. If(b2 < 0, " - ", " + ") → sign2
  67. If(b3 < 0, " - ", " + ") → sign3
  68. If(b4 < 0, " - ", " + ") → sign4
  69. If(b5 < 0, " - ", " + ") → sign5
  70. If(b6 < 0, " - ", " + ") → sign6
  71. If(showAnswers ≟ true, (("y = " * coef1) * "x²"), "y") → yText1
  72. If(showAnswers ≟ true, (("y = " * coef2) * "x²"), "y") → yText2
  73. If(showAnswers ≟ true, (("y = " * coef3) * "x²"), "y") → yText3
  74. If(showAnswers ≟ true, (("y = " * coef4) * "x²"), "y") → yText4
  75. If(showAnswers ≟ true, (("y = " * coef5) * "x²"), "y") → yText5
  76. If(showAnswers ≟ true, (("y = " * coef6) * "x²"), "y") → yText6
  77. TableText({{A1, B1}, {A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}}, "|_") → Table1
  78. TableText({{D1, E1}, {D2, E2}, {D3, E3}, {D4, E4}, {D5, E5}, {D6, E6}, {D7, E7}}, "|_") → Table2
  79. TableText({{G1, H1}, {G2, H2}, {G3, H3}, {G4, H4}, {G5, H5}, {G6, H6}, {G7, H7}}, "|_") → Table3
  80. TableText({{J1, K1}, {J2, K2}, {J3, K3}, {J4, K4}, {J5, K5}, {J6, K6}, {J7, K7}}, "|_") → Table4
  81. TableText({{M1, N1}, {M2, N2}, {M3, N3}, {M4, N4}, {M5, N5}, {M6, N6}, {M7, N7}}, "|_") → Table5
  82. TableText({{P1, Q1}, {P2, Q2}, {P3, Q3}, {P4, Q4}, {P5, Q5}, {P6, Q6}, {P7, Q7}}, "|_") → Table6

AI 绘图提示语参考

绘制一个图表，展示如何将表格数据转换为线性函数方程。首先生成两组对称数据，排序后随机选取系数，结合这些系数和常数项创建多个线性函数图像。每个函数用不同的颜色和标记表示，并标注关键点，最后展示函数图像与数据点的关系，体现函数方程的构建过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。