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指数函数的水平和垂直平移

指数函数的水平和垂直平移
几何画板及绘图内容加载中，请稍等……
2019-03-19 22:47
函数解析几何变换函数图像
本范例演示了指数函数的水平和垂直平移。核心数学概念包括函数变换、平移变换。通过使用GeoGebra命令如Sequence、Segment、If等，可以动态展示函数图像的平移效果。适合高中数学教学，帮助学生理解函数图像变换的基本原理。

GeoGebra 命令及参数

  1. LaTeX(If[kValCorrect > 0, ("+" * kValCorrect), If[kValCorrect ≟ 0, "", ("-" * abs(kValCorrect))]]) → DisplayPlusK
  2. Random(-5, 5) → hValCorrect
  3. LaTeX(If[hValCorrect > 0, ("-" * hValCorrect), If[hValCorrect ≟ 0, "", ("+" * abs(hValCorrect))]]) → DisplayMinusH
  4. Shuffle({1 / 4, 1 / 3, 1 / 2, 2, 3, 4}) → potentialBaseValues
  5. Element(potentialBaseValues, 1) → base
  6. If(IsInteger[base], ("\vphantom{\frac{1}{1}}" * base), (("\left(" * FractionText[base]) * "\right)")) → baseDisplay
  7. Polygon({(-10.5, -10.5), (-10.5, 10.5), (10.5, 10.5), (10.5, -10.5)}) → viewBox
  8. LaTeX(((((("\vphantom{\frac{1}{1}}y=" * baseDisplay) * "^{x") * DisplayMinusH) * "}") * DisplayPlusK)) → translatedFuncLbl
  9. LaTeX(((MainInstruc * "\\") * SpecInstruc)) → InstructionsComplete
  10. LaTeX((UnicodeToLetter[10007] * "\text{ Incorrect}")) → incorrect
  11. LaTeX((UnicodeToLetter[10003] * "\text{ Correct}")) → correct
  12. LaTeX(If[hValUser > 0, ("-" * hValUser), If[hValUser ≟ 0, "", ("+" * abs(hValUser))]]) → DisplayUserMinusH
  13. LaTeX(If[kValUser > 0, ("+" * kValUser), If[kValUser ≟ 0, "", ("-" * abs(kValUser))]]) → DisplayUserPlusK
  14. LaTeX(((((baseDisplay * "^{x ") * DisplayUserMinusH) * "} ") * DisplayUserPlusK)) → userFunctionTxt
  15. LaTeX(If[kValCorrect ≟ 0, "", (((("a vertical translation of " * abs(kValCorrect)) * " unit") * If[abs(kValCorrect) > 1, "s ", " "]) * If[kValCorrect < 0, "\\down", "\\up"])]) → fbVertical
  16. LaTeX(If[hValCorrect ≟ 0, "", ((((("a horizontal translation of " * abs(hValCorrect)) * " unit") * If[abs(hValCorrect) > 1, "s", ""]) * "\\to the") * If[hValCorrect > 0, " right", " left"])]) → fbHorizontal
  17. Sequence((11, i), i, 9, 1, -4) → legendAnchors
  18. Segment(Element[legendAnchors, 1], Element[legendAnchors, 1] + (3, 0)) → legend1
  19. Segment(Element[legendAnchors, 2], Element[legendAnchors, 2] + (3, 0)) → legend2
  20. LaTeX((((((((("\text{In order to transform \(" * parentFuncLbl) * "\) into \\\(") * translatedFuncLbl) * "\), we must apply \\") * fbHorizontal) * If[hAndv, ", and ", ""]) * fbVertical) * ".}")) → fbComplete