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分段函数问题36

分段函数问题36
几何画板及绘图内容加载中，请稍等……
2017-01-16 03:30
函数微积分几何作图函数图像
①本范例演示了分段函数的图形绘制与性质分析；②涉及核心数学概念包括函数、分段函数、导数、切线函数、根、勾股定理及二项分布；③作图要点提炼自构造摘要，使用了Vector（向量）、Segment（线段）、FractionText（分数文本）、Intersect（交点）等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解复杂函数的图像特征与计算方法。

GeoGebra 命令及参数

  1. Vector((0, 0), (-10.9, 0)) → v_2
  2. Vector((0, 0), (10.9, 0)) → v_3
  3. Vector((0, 0), (0, 10.9)) → v_4
  4. Vector((0, 0), (0, -10.9)) → v_1
  5. Segment((-10, 10), (10, 10)) → s_{10}
  6. Segment((-10, 9), (10, 9)) → s_{14}
  7. Segment((-10, 8), (10, 8)) → s_{17}
  8. Segment((-10, 7), (10, 7)) → s_{20}
  9. Segment((-10, 6), (10, 6)) → s_{22}
  10. Segment((-10, 5), (10, 5)) → s_{24}
  11. Segment((-10, 4), (10, 4)) → s_{26}
  12. Segment((-10, 3), (10, 3)) → s_{28}
  13. Segment((-10, 2), (10, 2)) → s_{30}
  14. Segment((-10, 1), (10, 1)) → s_{32}
  15. Segment((-10, -10), (10, -10)) → s_{34}
  16. Segment((-10, -9), (10, -9)) → s_{36}
  17. Segment((-10, -8), (10, -8)) → s_{37}
  18. Segment((-10, -7), (10, -7)) → s_{39}
  19. Segment((-10, -6), (10, -6)) → s_2
  20. Segment((-10, -5), (10, -5)) → s_4
  21. Segment((-10, -4), (10, -4)) → s_6
  22. Segment((-10, -3), (10, -3)) → s_8
  23. Segment((-10, -2), (10, -2)) → s_{11}
  24. Segment((-10, -1), (10, -1)) → s_{15}
  25. Segment((-10, -10), (-10, 10)) → s_{18}
  26. Segment((-9, -10), (-9, 10)) → s_{21}
  27. Segment((-8, -10), (-8, 10)) → s_{23}
  28. Segment((-7, -10), (-7, 10)) → s_{25}
  29. Segment((-6, -10), (-6, 10)) → s_{27}
  30. Segment((-5, -10), (-5, 10)) → s_{29}
  31. Segment((-4, -10), (-4, 10)) → s_{31}
  32. Segment((-3, -10), (-3, 10)) → s_{33}
  33. Segment((-2, -10), (-2, 10)) → s_{35}
  34. Segment((-1, -10), (-1, 10)) → s_{12}
  35. Segment((10, -10), (10, 10)) → s_{38}
  36. Segment((9, -10), (9, 10)) → s_{40}
  37. Segment((8, -10), (8, 10)) → s_1
  38. Segment((7, -10), (7, 10)) → s_3
  39. Segment((6, -10), (6, 10)) → s_5
  40. Segment((5, -10), (5, 10)) → s_7
  41. Segment((4, -10), (4, 10)) → s_9
  42. Segment((3, -10), (3, 10)) → s_{13}
  43. Segment((2, -10), (2, 10)) → s_{16}
  44. Segment((1, -10), (1, 10)) → s_{19}
  45. FractionText(g_1) → text4
  46. FractionText(g_1) → text6
  47. Intersect(h_1, l, (5.5, 10)) → A
  48. Intersect(h_1, n, (10, 19)) → B
  49. Intersect(h_1, i, (4, -10)) → C
  50. Intersect(h_2, l, (-6, 10)) → D
  51. Intersect(h_2, i, (-4.5, -10)) → E
  52. Intersect(h_2, m, (-10, -21)) → F
  53. Intersect(k_4, l, (-3.316624790196715, 9.999999998947406)) → G
  54. Intersect(k_3, l, (3.3166247903562325, 10.000000000005523)) → H
  55. Intersect(k_1, i, (2.999999999576448, -9.999999997458689)) → I
  56. Intersect(k_2, i, (-2.999999999576448, -9.999999997458689)) → J
  57. Intersect(If[x > b, (f_1 * x) + f_2], k_1, (-16.212701635481952, -3.0907924465267502)) → K
  58. Intersect(g, l) → L
  59. Intersect(g, i) → M
  60. Intersect(g, m) → N
  61. Intersect(g, n) → O

AI 绘图提示语参考

绘制一个坐标网格，范围从负十到正十，包含水平和垂直的网格线，每条线间隔一个单位。在网格上，用箭头表示坐标轴的正方向和负方向，从原点出发分别指向左右和上下。此外，在网格上方或附近放置两个分数文本，内容为某个函数的分数形式。最后，在网格上标记两个交点：一个位于上半区域，另一个位于更上方，分别由一条水平曲线和两条不同斜率的直线相交产生。整体图形用于展示分段函数的图像及其相关分析。
以上提示语为根据原始绘图命令整理而来，仅供参考。