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函数加法示例

函数加法示例
几何画板及绘图内容加载中，请稍等……
2015-09-25 23:36
函数解析几何滑块动画
所属专题 CCSS Support Math II Unit 2
本示例演示了如何通过给定的线性函数f(x) = 4x + 1和g(x) = 3x - 6，构造一个新的函数h(x) = (f + g)(x)。核心数学概念包括函数的加法。构造摘要中提到了使用了Border, Gear, Book等对象。适合初中及以上学生学习函数的基本运算。

GeoGebra 命令及参数

  1. SelectedElement(FXC) → FXCV
  2. SelectedElement(FXX) → FXXV
  3. SelectedElement(GXC) → GXCV
  4. SelectedElement(GXX) → GXXV
  5. LaTeX("\text{Constant of f(x):}") → DKT2
  6. LaTeX("\text{Constant of g(x):}") → DKT4
  7. LaTeX("\text{Add the two functions.}") → PG1B
  8. LaTeX("\text{\textcolor{#000099}{h(x) = (f + g)(x) = f(x) + g(x)}}") → Pg1C
  9. LaTeX("\text{Combine like terms.}") → PG2A
  10. LaTeX("\text{Clear the parentheses and reorder the expression, then combine like terms.}") → PG2B
  11. LaTeX((((((((("\text{\textcolor{#000099}{h(x) = (" * FXXV) * "x + ") * FXCV) * ") + (") * GXXV) * "x ") * GXCV) * ")}}")) → Pg2C
  12. LaTeX("\text{Equation for \textcolor{#000099}{h(x)}}") → Pg2D
  13. LaTeX((((((((("\text{\textcolor{#000099}{h(x) = " * FXXV) * "x + ") * FXCV) * " + ") * GXXV) * "x ") * GXCV) * "}}")) → text1
  14. LaTeX("\text{Remove the parentheses.}") → Pg2F
  15. LaTeX("\text{Rearrange to group like terms.}") → Pg2H
  16. LaTeX((((((((("\text{\textcolor{#000099}{h(x) = " * FXXV) * "x + ") * GXXV) * "x + ") * FXCV) * " ") * GXCV) * "}}")) → Pg2G
  17. LaTeX((((("\text{\textcolor{#000099}{h(x) = " * ADDX) * "x ") * MinusX) * "}}")) → Pg2I
  18. LaTeX("\text{Combine like terms.}") → PG2J
  19. LaTeX("\text{where \textcolor{#000099}{a ≠ 0}. The graph of any quadratic function is a parabola.}") → WTK2
  20. LaTeX((((((((("\text{Given \textcolor{#000099}{f(x) = " * FXXV) * "x + ") * FXCV) * "} and \textcolor{#000099}{g(x) = ") * GXXV) * "x ") * GXCV) * "}, build a new function \textcolor{#000099}{h(x)}, for which \textcolor{#000099}{h(x) = (f + g)(x)}.}")) → Pg1A
  21. LaTeX((((((((((((((((("\text{Because \textcolor{#000099}{f(x) = " * FXXV) * "x + ") * FXCV) * "} and \textcolor{#000099}{g(x) = ") * GXXV) * "x ") * GXCV) * "}, adding \textcolor{#000099}{f(x)} and \textcolor{#000099}{g(x)} results in \textcolor{#000099}{h(x) = (f + g)(x) = (") * FXXV) * "x + ") * FXCV) * ") + (") * GXXV) * "x ") * GXCV) * ")}.}")) → PG1D
  22. LaTeX((((((((((((("\text{The result of adding \textcolor{#000099}{f(x) = " * FXXV) * "x + ") * FXCV) * "} and \textcolor{#000099}{g(x) = ") * GXXV) * "x ") * GXCV) * "} is \textcolor{#000099}{h(x) = ") * ADDX) * "x ") * MinusX) * "}.}")) → text2
  23. LaTeX("\text{\mathbf{quadratic\;function} a function that can be written in the form \textcolor{#000099}{f(x) = ax^2 + bx + c},}") → WTK1
  24. LaTeX("\text{x-value of f(x):}") → DKT1
  25. LaTeX("\text{x-value of g(x):}") → DKT3