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校报成本核算——线性函数入门练习

校报成本核算——线性函数入门练习
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2025-12-17 19:31
所属专题 Lineare Funktionen
该GeoGebra范例以学校校报印刷成本为情境，演示线性函数f(x)=1.95x+15如何描述总成本与印刷份数之间的关系。核心数学概念是线性函数的参数含义：斜率1.95表示每份印刷的边际成本（单位变动成本），截距15表示固定成本（如排版费）。范例包含多个交互式问题，如判断正确函数表达式、根据无固定成本条件写出函数式，以及讨论“印刷量翻倍价格是否翻倍”的常见误解。作图要点：使用Sequence、Element、Textfield、Join、Segment、If、Corner、Circle、Text、Flatten、Point、RotateText等GeoGebra命令构建了包含按钮、输入框、反馈区域和步骤计数器的动态练习环境，并利用RasterPixMat等对象实现网格显示。适合初中7-8年级学生，用于理解线性函数图像与方程之间的转换，以及参数k和d的实际意义，可作为课堂探究或课后练习材料。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {10, 2, 10, 5, 10, 7, 6, 2, 3, 1}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  5. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  6. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  7. Segment(Origin + ((minX / stepX * disX) - edgeAxisX, 0), Origin + ((maxX / stepX * disX) + edgeAxisX, 0)) → segAxisX
  8. Segment(Origin + (0, (minY / stepY * disY) - edgeAxisY), Origin + (0, (maxY / stepY * disY) + edgeAxisY)) → segAxisY
  9. Sequence(Origin + ((minX / stepX * disX), 0) + (k * (disX, 0)), k, 0, maxX / stepX - minX / stepX) → PointsXAxis
  10. Sequence(Origin + (0, (minY / stepY * disY)) + (k * (0, disY)), k, 0, maxY / stepY - minY / stepY) → PointsYAxis
  11. Sequence(Segment[PointsXAxis(k) + (0, (-disSeg)), PointsXAxis(k) + (0, disSeg)], k, 1, Length[PointsXAxis]) → segXAxis
  12. Sequence(Segment[PointsYAxis(k) + ((-disSeg), 0), PointsYAxis(k) + (disSeg, 0)], k, 1, Length[PointsYAxis]) → segYAxis
  13. Sequence(m, m, minX, maxX, stepX) → numbersXAxis
  14. Sequence(Text[((("\textsf{\footnotesize{\(" * If[numbersXAxis(k) ≥ 0, "\phantom{\(-\)}", ""]) * If[Element[numbersXAxis, k] ≟ 0, "", ("" * Element[numbersXAxis, k])]) * "\)}}"), PointsXAxis(k) + (-0.12, (-disSeg)), false, true, 0, -1], k, 1, (maxX - minX) / stepX + 1) → CapX
  15. Sequence(m, m, minY, maxY, stepY) → numbersYAxis
  16. Sequence(Text[((("\textsf{\footnotesize{\(" * If[numbersYAxis(k) ≥ 0, "\phantom{\(-\)}", ""]) * If[Element[numbersYAxis, k] ≟ 0, "", ("" * Element[numbersYAxis, k])]) * "\)}}"), PointsYAxis(k) + ((-disSeg) + 0.05, 0), false, true, -1, 0], k, 1, (maxY - minY) / stepY + 1) → CapY
  17. Element({Polygon[(x(PointsXAxis(1)), y(PointsYAxis(1))) + ((-edgeAxisX) - 0.05, (-edgeAxisY) - 0.05), (x(PointsXAxis(Length[PointsXAxis])), y(PointsYAxis(1))) + (edgeAxisX + 0.05, (-edgeAxisY) - 0.05), (x(PointsXAxis(Length[PointsXAxis])), y(PointsYAxis(Length[PointsYAxis]))) + (edgeAxisX + 0.05, edgeAxisY + 0.05), (x(PointsXAxis(1)), y(PointsYAxis(Length[PointsYAxis]))) + ((-edgeAxisX) - 0.05, edgeAxisY + 0.05)]}, 1) → polyAxis
  18. Sequence(Sequence[(x(PointsXAxis(k)), y(PointsYAxis(m))), k, 1, Length[PointsXAxis]], m, 1, Length[PointsYAxis]) → AllPointsOnGrid
  19. If(step ≤ 4, (0, 7.5), (0, 5.25)) → PosTable
  20. Sequence(Sequence[PosTable + (Sum[ListSpalte, k], (-Sum[ListZeile, m])), k, 0, 2], m, 0, 8) → TablePosMat
  21. Segment(Point031, Point031 + (anim04 * (Point036 + (edgeAxisX, edgeAxisY) - Point031))) → segGraph04
  22. Textfield(input021) → InputBox021
  23. Textfield(input022) → InputBox022
  24. Textfield(input023) → InputBox023
  25. Textfield(input024) → InputBox024
  26. Textfield(input051) → InputBox051
  27. Textfield(input052) → InputBox052
  28. Corner(imgLupe, 3) → PosImgLupe3
  29. Circle(MPLupe, (0.5 * radiusLupe)) → circleLupe
  30. Text("\textsf{\bold{Zieh mich!}}", PosImgLupe2, false, true, 0, 0) → CapLupe
  31. Sequence(Midpoint[TablePosMat(2 + k, 3), TablePosMat(3 + k, 3)] + (0.6, 0), k, 0, 6) → Park03
  32. Flatten(AllPointsOnGrid) → GridPoints
  33. Point(Join[{{Park03(4)}, GridPoints}]) → Pos033
  34. Point(Join[{{Park03(5)}, GridPoints}]) → Pos034
  35. Point(Join[{{Park03(6)}, GridPoints}]) → Pos035
  36. Point(Join[{{Park03(7)}, GridPoints}]) → Pos036
  37. Point(Join[{{Park03(1)}, GridPoints}]) → Pos031
  38. If(step ≟ 4, anim04 ≟ 0 ∨ anim04 ≟ 1, true) → clickableBtnBack
  39. If(step ≟ 2, correct021 ∧ correct022 ∧ correct023 ∧ correct024, step ≟ 3, Sort[AllPos03] ≟ Sort[SolPoints] ∧ showFB031 ∧ showFB033 ∧ showFB034 ∧ showFB035 ∧ showFB036, step ≟ 4, anim04 ≟ 1, step ≟ 5.2, correct051 ∧ correct052, true) → clickableBtnNext
  40. RotateText(Text["\textsf{\bold{\footnotesize{Zieh mich!}}}", Park03(2) + (0.1, 0.1), false, true, 0, 0], 90°) → CapZiehMich03