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线性不等式探究

线性不等式探究
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2016-01-06 00:52
函数解析几何不等式
本范例通过四条直线帮助学生探究线性不等式。核心数学概念包括线性不等式的表示与解集。构造摘要中使用了Textfield, If, TextToUnicode等GeoGebra命令，涉及线性不等式的表示与解集的动态演示。适合高中数学教学与学习。

GeoGebra 命令及参数

  1. Textfield(m_1) → inputBox1
  2. Textfield(c_1) → inputBox2
  3. Textfield(m_2) → inputBox3
  4. Textfield(c_2) → inputBox4
  5. If(S_1 ≟ 1, If[t_1, "≥", ">"], If[S_1 ≟ -1, If[t_1, "≤", "<"], "="]) → sgn_1
  6. If(S_1 ≟ 1, y > f_1(x), If[S_1 ≟ -1, y < f_1(x), y = f_1(x)]) → C1
  7. If(S_2 ≟ 1, If[t_2, "≥", ">"], If[S_2 ≟ -1, If[t_2, "≤", "<"], "="]) → sgn_2
  8. If(S_2 ≟ 1, y > f_2(x), If[S_2 ≟ -1, y < f_2(x), y = f_2(x)]) → C2
  9. Textfield(c_3) → inputBox5
  10. If(S_3 ≟ 1, y > (0 * x) + c_3, If[S_3 ≟ -1, y < (0 * x) + c_3, y = (0 * x) + c_3]) → C3
  11. If(S_3 ≟ 1, If[t_3, "≥", ">"], If[S_3 ≟ -1, If[t_3, "≤", "<"], "="]) → sgn_3
  12. Textfield(d_1) → inputBox6
  13. If(S_4 ≟ 1, x > (0 * y) + d_1, If[S_4 ≟ -1, x < (0 * y) + d_1, x = (0 * y) + d_1]) → C4
  14. If(S_4 ≟ 1, If[t_4, "≥", ">"], If[S_4 ≟ -1, If[t_4, "≤", "<"], "="]) → sgn_4
  15. Textfield(m_1) → inputBox1_1
  16. Textfield(c_1) → inputBox2_1
  17. TextToUnicode("≤") → q
  18. Textfield(m_2) → inputBox3_1
  19. Textfield(c_2) → inputBox4_1
  20. If(a ∧ b ∧ c ∧ d, C1(x, y) ∧ C2(x, y) ∧ C3(x, y) ∧ C4(x, y), If[a ∧ b ∧ c, C1(x, y) ∧ C2(x, y) ∧ C3(x, y), If[a ∧ b ∧ d, C1(x, y) ∧ C2(x, y) ∧ C4(x, y), If[a ∧ c ∧ d, C1(x, y) ∧ C3(x, y) ∧ C4(x, y), If[b ∧ c ∧ d, C2(x, y) ∧ C3(x, y) ∧ C4(x, y)]]]]) → OverlapOfAll