线性函数与方程的交互演示

线性函数与方程的交互演示
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2017-08-01 00:54
①本范例演示线性函数图像、方程求解及与几何图形的交点关系;②涉及核心数学概念包括线性方程、函数、几何变换(如缩放)、交集计算;③构造中运用了Zip, LaTeX, Corner, TableText, PolyLine, Intersect, Midpoint, Vector等GeoGebra命令与对象;④适合高中数学教学,用于理解函数变换、方程求解及几何直观。

GeoGebra 命令及参数

  1. Zip(f(k), k, xlist) → ylist
  2. LaTeX(steps) → counter
  3. LaTeX("\text{Move the slider to solve the problem.}") → text0
  4. LaTeX("\text{Use the buttons below to return to the original}\cr\text{problem or randomly generate a similar practice}\cr\text{problem.}") → RandomizationText
  5. Corner(2, 3) → topright
  6. Corner(2, 1) → bottomleft
  7. LaTeX((("\text{Graph the solution set for the linear equation }\cr\textcolor{#000099}{" * f) * "}.")) → Problem
  8. LaTeX("\text{Make a table. Choose at least three values for }\textcolor{#000099}{x}\text{, and}\cr\text{find the corresponding values of }\textcolor{#000099}{y}\text{ using the given}\cr\text{equation.}") → text1
  9. TableText({Append["\textcolor{#000099}{x}", xlist], Append["\textcolor{#000099}{y}", ylist]}, "vc") → text2
  10. LaTeX("\text{Plot the ordered pairs on the coordinate plane.}") → text3
  11. Zip((j, k), j, xlist, k, ylist) → pointslist
  12. Corner(2, 2) → bottomright
  13. Corner(2, 4) → topleft
  14. PolyLine(bottomleft, bottomright, topright, topleft, bottomleft) → frame
  15. Intersect(f, frame) → A, B
  16. Midpoint(A, B) → middle
  17. Vector(middle, B) → lazyarrow1
  18. Vector(middle, A) → lazyarrow2
  19. LaTeX((("\text{The solution set for }\textcolor{#000099}{" * f) * "}\text{ is a straight line.}\cr\text{Connect the points by drawing a line through them.}\cr\text{Use arrows at each end of the line to demonstrate}\cr\text{that the line continues infinitely in each direction.}\cr\text{This represents all the solutions for the equation.}")) → text4