GeoGebra数学范例:多函数与几何作图

GeoGebra数学范例:多函数与几何作图
几何画板及绘图内容加载中,请稍等……
2023-02-15 22:10
所属专题 Function Arts
本范例通过GeoGebra演示多函数图像与几何作图关系。核心数学概念包括幂函数、三角函数、条件概率及微分学。作图要点涉及A、B、f、g、h等对象的构造,以及f₁、g₁等参数的调整。适合高中生学习函数图像变换与几何直观应用。

GeoGebra 命令及参数

  1. (-5.872, 0.118)
  2. (6.1, 0.11)
  3. f(x) = ((x + 3) * 0.429) + 0.7
  4. g(x) = If[-3 ≤ x ≤ 6, f(x)]
  5. h(x) = (0.13 * (x + 4.5)^(2)) + 0.4
  6. p(x) = If[-4.5 ≤ x ≤ -3, h(x)]
  7. q(x) = (0.5 * (x + 4.5)^(2)) + 0.4
  8. r(x) = If[-5.6 ≤ x ≤ -4.5, q(x)]
  9. s(x) = (3.8 * (x + 5.4)^(2)) + 0.87
  10. f_{1}(x) = (4.9 * sin(x + 6.55)) - 1.7
  11. g_{1}(x) = If[-5.83 ≤ x ≤ -5.4, f_{1}(x)]
  12. h_{1}(x) = (1.5 * (x + 5.4)) + 2.8
  13. p_{1}(x) = If[-5.4 ≤ x ≤ -4.4, h_{1}(x)]
  14. q_{1}(x) = (3 * (x + 4.6)) + 3.6
  15. r_{1}(x) = If[-4.6 ≤ x ≤ -4.36, q_{1}(x)]
  16. s_{1}(x) = (19 * (x + 4.4)^(2)) + 2.7
  17. t_{1}(x) = If[-4.615 ≤ x ≤ -4.4, s_{1}(x)]
  18. f_{2}(x) = (0.49 * (x + 3.4)^(2)) + 2.2
  19. g_{2}(x) = If[-4.4 ≤ x ≤ -3.4, f_{2}(x)]
  20. h_{2}(x) = (0.268 * (x + 3)) + 2.2
  21. p_{2}(x) = If[-3 ≤ x ≤ 6, h_{2}(x)]
  22. q_{2}(x) = (0 * (x + 3.4)) + 2.2
  23. r_{2}(x) = If[-3.4 ≤ x ≤ -3, q_{2}(x)]
  24. s_{2}(x) = (2.6 * (x + 4.2)) + 3.4
  25. t(x) = If[-5.81 ≤ x ≤ -5.5, s(x)]
  26. f_{3}(x) = (2.6 * (x + 3.42)) + 3.4
  27. g_{3}(x) = If[-3.43 ≤ x ≤ -2.94, f_{3}(x)]
  28. h_{3}(x) = (0 * (x + 4.2)) + 3.38
  29. p_{3}(x) = If[-4.2 ≤ x ≤ -3.4, h_{3}(x)]
  30. q_{3}(x) = (0 * (x + 3)) + 6.54
  31. r_{3}(x) = If[-3 ≤ x ≤ -2.2, q_{3}(x)]
  32. s_{3}(x) = (16 * (x + 2.3)) + 5.1
  33. t_{3}(x) = If[-2.3 ≤ x ≤ -2.21, s_{3}(x)]
  34. f_{4}(x) = (16 * (x + 3)) + 3.4
  35. g_{4}(x) = If[-3 ≤ x ≤ -2.92, f_{4}(x)]
  36. h_{4}(x) = (0 * (x + 3)) + 3.4
  37. p_{4}(x) = If[-3 ≤ x ≤ -2.2, h_{4}(x)]
  38. q_{4}(x) = (2.8 * (x + 2.27)) + 5.1
  39. r_{4}(x) = If[-2.3 ≤ x ≤ -1.76, q_{4}(x)]
  40. s_{4}(x) = (2.6 * (x + 2.2)) + 3.4
  41. f_{5}(x) = (0 * (x + 1.8)) + 6.57
  42. g_{5}(x) = If[-1.76 ≤ x ≤ -1, f_{5}(x)]
  43. h_{5}(x) = (2.6 * (x + 2.1)) + 3.4
  44. p_{5}(x) = If[-2.1 ≤ x ≤ -0.9, h_{5}(x)]
  45. q_{5}(x) = (2.6 * (x + 1.38)) + 3.4
  46. r_{5}(x) = If[-1.38 ≤ x ≤ -0.18, q_{5}(x)]
  47. s_{5}(x) = (0 * (x + 1.2)) + 3.4
  48. t_{5}(x) = If[-2.1 ≤ x ≤ -1.4, s_{5}(x)]
  49. f_{6}(x) = (0 * (x + 0.9)) + 6.57
  50. h_{6}(x) = (2.7 * (x + 1.2)) + 3.4
  51. p_{6}(x) = If[-1.2 ≤ x ≤ -0.05, h_{6}(x)]
  52. g_{6}(x) = If[-0.9 ≤ x ≤ -0.16, f_{6}(x)]
  53. q_{6}(x) = (2.6 * (x + 0.45)) + 3.4
  54. r_{6}(x) = If[-0.45 ≤ x ≤ 0.04, q_{6}(x)]
  55. s_{6}(x) = (2.6 * (x - 04)) + 15
  56. t_{2}(x) = If[-4.2 ≤ x ≤ -3, s_{2}(x)]
  57. t_{6}(x) = If[0.4 ≤ x ≤ 0.75, s_{6}(x)]
  58. f_{7}(x) = (-24 * (x - 0.15)) + 3.3
  59. g_{7}(x) = If[0.09 ≤ x ≤ 0.147, f_{7}(x)]
  60. h_{7}(x) = (-22 * (x - 1))

AI 绘图提示语参考

绘制包含多个函数图像的图形,展示幂函数、三角函数与几何构造的关系。主要对象包括分段定义的函数 f、g、h 及其变形,以及基于条件概率的几何曲线。先画出基础函数曲线,再添加条件控制的几何对象,最后叠加三角函数图像,体现函数变换与几何直观。
以上提示语为根据原始绘图命令整理而来,仅供参考。