函数的定义域与值域 by Breck Jacobs

函数的定义域与值域 by Breck Jacobs
几何画板及绘图内容加载中,请稍等……
2016-03-05 03:45
①本范例演示了如何通过 GeoGebra 绘制函数的定义域与值域图形;②涉及的核心数学概念包括函数、定义域、值域、几何作图;③作图要点——从下方『构造摘要』提炼用到了 If, Min, Max, Intersect, Vector, Defined, Segment, IndexOf, Polygon 等GeoGebra命令/对象;④适合高中数学教学或自学,用于理解函数图像与性质。

GeoGebra 命令及参数

  1. If(a, L, If[b, (1.5, 0), If[c, (1, 0)]]) → L1
  2. If(a, g1, If[b, g2, If[c, g3]]) → f
  3. Min(f, x(L1), rght) → mi11
  4. If(b, (0, 0), If[c, (0.5, 0), If[a, R]]) → R1
  5. Min(f, lft, x(R1)) → mig1
  6. Min(list2) → min_f
  7. Max(f, lft, x(R1)) → mag2
  8. Min(f, x(mag2), x(R1)) → mi_2
  9. Min(y(mi_2), x(mi11)) → MiE
  10. Intersect(f, j, x(mag2), x(mi_2)) → E
  11. Intersect(d, xAxis) → C
  12. Intersect(f, d, (-3, -1.7999999999999998)) → A
  13. Vector(A, B) → u
  14. Defined(A) → e
  15. If(x(L1) ≤ x1, If[x1 < x(R), B, R], L1) → end2
  16. Segment(L1, end2) → h
  17. If(lft ≤ x1, If[x1 < x(R1), B, R1], L) → end1
  18. Segment(L, end1) → g
  19. Intersect(f, j, lft, x(mag2)) → D
  20. Vector((x(L), f(x(L))), L) → v
  21. Vector((x(R), f(x(R))), R) → w
  22. Vector((x(L1), f(x(L1))), L1) → z
  23. Vector((x(R1), f(x(R1))), R1) → l
  24. Max(f, x(L1), rght) → mag22
  25. Max(list1) → max_f
  26. Vector((min_f, f(min_f)), (0, f(min_f))) → r
  27. If(min_f ≤ y1, If[y1 < y(mag2), M, (0, y(mag2))], Y_l) → endv1
  28. Segment(Y_l, endv1) → t
  29. Vector(D, (0, y(D))) → n
  30. IndexOf(max_f, list1) → Ind_ma
  31. IndexOf(min_f, list2) → Ind_mi
  32. Vector(MiPt, (0, y(MiPt))) → v_1
  33. Vector(MaPt, (0, y(MaPt))) → u_1
  34. If(L1 ≠ L, Intersect[f, j, x(L1), rght], Intersect[f, j, x(mi_2), rght]) → F
  35. Vector(E, (0, y(E))) → p
  36. Vector(F, (0, y(F))) → q
  37. If(min_f ≤ y1, If[y1 < y(mag2), (0, y(E)), (0, y(mag2))], (0, MiE)) → endv2
  38. Segment((0, MiE), endv2) → a_1
  39. If(min_f ≤ y1, If[y1 < y(mag22), (0, y(F)), (0, y(mag22))], (0, f(L1))) → endv3
  40. Segment((0, y(L1)), endv3) → b_1
  41. Segment((0, f(L1)), endv3) → c_1
  42. Polygon(Corner[1], (x(Corner[1]) + (0.3 * Distance[Corner[1], Corner[2]]), y(Corner[1])), (x(Corner[4]) + (0.3 * Distance[Corner[1], Corner[2]]), y(Corner[4])), Corner[4]) → poly1, d_1, e_1, f_1, g_1

AI 绘图提示语参考

绘制一个函数的图像,并标出其定义域和值域。首先绘制函数图像,然后使用条件语句确定定义域的边界点L1和R1,接着找到函数在这些边界点的值,用这些值构造水平线段表示值域。最后,通过条件语句和向量构造定义域和值域的边界线段,以及定义域和值域的交点。
以上提示语为根据原始绘图命令整理而来,仅供参考。