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利用图形解方程与不等式

利用图形解方程与不等式
几何画板及绘图内容加载中，请稍等……
2018-07-08 01:26
函数不等式函数图像
本范例通过图形展示如何解方程与不等式。它涉及方程、不等式的核心概念，以及如何使用GeoGebra命令构造图形。通过随机选取方程、不等式、线性、二次、三次及根式方程，展示了解方程与不等式的多种方法。适合高中数学教学与学习。

GeoGebra 命令及参数

  1. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → lina
  2. Random(-5, 5) → linsol
  3. Intersect(lineq, y = 0) → linint
  4. Random(-5, 5) → quadsol1
  5. Random(-5, 5) → quadsol2
  6. Intersect(quadeq, y = 0) → quadint1, quadint2
  7. Random(-5, 5) → cubsol1
  8. Random(-5, 5) → cubsol2
  9. Random(-5, 5) → cubsol3
  10. Intersect(cubeq, y = 0) → cubint1, cubint2, cubint3
  11. Random(-5, 5) → radsol
  12. Intersect(radeq, y = 0, (-3, 0)) → radint
  13. Random(1, 4) → ineq
  14. Ray(linint, (-10, 0)) → linleft
  15. Ray(linint, (10, 0)) → linright
  16. Intersect(lineq, y = 0) → A
  17. Segment(quadint1, quadint2) → f
  18. If(x(quadint1) < x(quadint2), Ray[quadint1, (-10, 0)], Ray[quadint2, (-10, 0)]) → quadleft
  19. If(x(quadint1) < x(quadint2), Ray[quadint2, (10, 0)], Ray[quadint1, (10, 0)]) → quadright
  20. Intersect(quadeq, y = 0) → B, C
  21. Ray(((-Max[{cubsol1, cubsol2, cubsol3}]), 0), (-10, 0)) → cubleft
  22. Ray(((-Min[{cubsol1, cubsol2, cubsol3}]), 0), (10, 0)) → cubright
  23. If((-cubsol1) < (-cubsol2) < (-cubsol3), Segment[((-cubsol1), 0), ((-cubsol2), 0)], (-cubsol3) < (-cubsol2) < (-cubsol1), Segment[((-cubsol3), 0), ((-cubsol2), 0)], (-cubsol1) < (-cubsol3) < (-cubsol2), Segment[((-cubsol1), 0), ((-cubsol3), 0)], (-cubsol2) < (-cubsol1) < (-cubsol3), Segment[((-cubsol2), 0), ((-cubsol1), 0)], (-cubsol2) < (-cubsol3) < (-cubsol1), Segment[((-cubsol2), 0), ((-cubsol3), 0)], (-cubsol3) < (-cubsol1) < (-cubsol2), Segment[((-cubsol3), 0), ((-cubsol1), 0)]) → h
  24. If((-cubsol1) < (-cubsol2) < (-cubsol3), Segment[((-cubsol2), 0), ((-cubsol3), 0)], (-cubsol3) < (-cubsol2) < (-cubsol1), Segment[((-cubsol2), 0), ((-cubsol1), 0)], (-cubsol1) < (-cubsol3) < (-cubsol2), Segment[((-cubsol3), 0), ((-cubsol2), 0)], (-cubsol2) < (-cubsol1) < (-cubsol3), Segment[((-cubsol1), 0), ((-cubsol3), 0)], (-cubsol2) < (-cubsol3) < (-cubsol1), Segment[((-cubsol3), 0), ((-cubsol1), 0)], (-cubsol3) < (-cubsol1) < (-cubsol2), Segment[((-cubsol1), 0), ((-cubsol2), 0)]) → i
  25. If(cubsol1 ≟ cubsol2 ∧ cubsol1 < cubsol3, Segment[((-cubsol1), 0), ((-cubsol3), 0)], cubsol1 ≟ cubsol3 ∧ cubsol1 < cubsol2, Segment[((-cubsol1), 0), ((-cubsol2), 0)], cubsol2 ≟ cubsol3 ∧ cubsol2 < cubsol1, Segment[((-cubsol2), 0), ((-cubsol1), 0)]) → j
  26. If(cubsol1 ≟ cubsol2 ∧ cubsol1 > cubsol3, Segment[((-cubsol1), 0), ((-cubsol3), 0)], cubsol1 ≟ cubsol3 ∧ cubsol1 > cubsol2, Segment[((-cubsol1), 0), ((-cubsol2), 0)], cubsol2 ≟ cubsol3 ∧ cubsol2 > cubsol1, Segment[((-cubsol2), 0), ((-cubsol1), 0)]) → k
  27. Intersect(cubeq, y = 0) → D, E, F
  28. Segment(((-rada), 0), (radsol, 0)) → l
  29. Ray((radsol, 0), (10, 0)) → m

AI 绘图提示语参考

绘制几个常见类型的函数图像，包括一条一次函数曲线、一条抛物线、一条三次函数曲线和一条根号函数曲线，分别在x轴上标出它们与坐标轴的交点；用射线和线段显示每个函数在x轴上的解区间，特别是一次函数从交点向左右两侧延伸，抛物线在两个交点之间有线段，两端向外延伸射线，三次函数的三个交点之间及其外侧分别用线段和射线表示，根号函数从负根到解之间有线段，解右侧有射线延伸。
以上提示语为根据原始绘图命令整理而来，仅供参考。