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函数的映射图示

函数的映射图示
几何画板及绘图内容加载中，请稍等……
2017-05-09 19:16
函数解析几何函数图像
这个范例展示了函数如何通过映射图而非图形来表示。它涉及函数的概念，特别是如何通过映射图来理解函数的输入和输出关系。使用了TableText, Corner, Distance, Line, Text, panelleft1, Textfield, If, Sequence, Vector, Zip等GeoGebra命令。适合高中数学教学，帮助学生直观理解函数的性质。

GeoGebra 命令及参数

  1. TableText({{"0"}, {"\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hc") → Xt0
  2. Corner(1) → corner1
  3. Corner(2) → corner2
  4. Corner(3) → corner3
  5. Corner(4) → corner4
  6. Corner(5) → screenDim
  7. Distance(corner1, corner2) → distX
  8. Distance(corner1, corner4) → distY
  9. Line(OY, yAxis) → YaxisLine
  10. Text("(x,y) = (" + (x(A)) + "," + (y(A)) + ") in black coordinate system") → text2
  11. Text("(X,Y) = (" + (x(A) - x(OY)) + "," + (y(A) - y(OY)) + ") in blue coordinate system") → text1
  12. panelleft1(panelsize) → panelquad, panelseg1, panelseg2, panelseg3, panelseg4, panelline
  13. Textfield(f) → InputBox1
  14. Line(OX, yAxis) → XaxisLine
  15. Textfield(x0) → InputBox2
  16. If(minstepfrac > lg(5), 10^(minsteppower + 1), If[minstepfrac > lg(2), (5 * 10^(minsteppower)), If[minstepfrac > 0, (2 * 10^(minsteppower)), 10^(minsteppower)]]) → stepsize
  17. Sequence(Text[TableText[{{"\phantom{(}" + (x0 + (n * stepsize)) + ""}, {"\phantom{(} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hr"], (x(OX) - Distance[Corner[Xt0, 1], Corner[Xt0, 2]] + 7 / unitX, (n * steplength) + y(OX) + (Distance[Corner[Xt0, 1], Corner[Xt0, 4]] * 0.25) + 4 / unitY), true, true], n, ceil((y(Corner[1]) - y(OX)) / steplength), floor((y(Corner[4]) - y(OX)) / steplength)) → XaxisNumbers
  18. Sequence(Segment[(x(OX), y(OX) + (n * steplength)), (x(OX) - 2 / unitX, y(OX) + (n * steplength))], n, ceil((y(Corner[1]) - y(OX)) / steplength), floor((y(Corner[4]) - y(OX)) / steplength)) → XaxisTicks
  19. Sequence(Text[TableText[{{"\phantom{(}" + (y0 + (n * stepsize)) + ""}, {"\phantom{(} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "}}, "hr"], (x(OY) - Distance[Corner[Xt0, 1], Corner[Xt0, 2]] + 7 / unitX, (n * steplength) + y(OY) + (Distance[Corner[Xt0, 1], Corner[Xt0, 4]] * 0.25) + 4 / unitY), true, true], n, ceil((y(Corner[1]) - y(OY)) / steplength), floor((y(Corner[4]) - y(OY)) / steplength)) → YaxisNumbers
  20. Sequence(Segment[(x(OY), y(OY) + (n * steplength)), (x(OY) - 2 / unitX, y(OY) + (n * steplength))], n, ceil((y(Corner[1]) - y(OY)) / steplength), floor((y(Corner[4]) - y(OY)) / steplength)) → YaxisTicks
  21. Vector((xpos, 0), (ypos, 0)) → u
  22. Sequence(i / spacing, i, ((-numarrows) * spacing), (numarrows * spacing)) → arrowstarts
  23. Zip(x0 + (as * numminstep), as, arrowstarts) → arrowxvals
  24. Zip(f(ax), ax, arrowxvals) → arrowyvals
  25. Zip((xpos, ((xv - x0) * steplength / stepsize)), xv, arrowxvals) → arrowxcoords
  26. Zip((ypos, ((yv - y0) * steplength / stepsize)), yv, arrowyvals) → arrowycoords
  27. Zip(Vector[ax, ay], ax, arrowxcoords, ay, arrowycoords) → arrows
  28. Zip(Line[ax, ay], ax, arrowxcoords, ay, arrowycoords) → lines
  29. Vector((xpos, 0), (ypos, 0)) → v

AI 绘图提示语参考

画一个函数映射图，展示函数的输入输出关系。包含两个坐标系，一个黑色一个蓝色，分别标示点的坐标。在横纵轴上按等距标注刻度，并用箭头连接输入和输出值，清晰展示函数映射过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。