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探索指数函数图像

探索指数函数图像
几何画板及绘图内容加载中，请稍等……
2019-02-08 04:40
函数微积分导数函数图像
①本范例演示指数函数图像随底数变化的动态特性；②涉及核心数学概念包括指数函数、函数图像变换、导数；③构造要点运用了GeoGebra命令如UnicodeToLetter、Polygon、TableText、LaTeX、Intersect、Sequence、Element、Segment等，以及对象如right、left、bottom、top、HowDidIDo、TryAnother、xmark、cmark等；④适合高中及以上数学学习者，用于理解指数函数性质及图像绘制技巧。

GeoGebra 命令及参数

  1. UnicodeToLetter(10007) → xmark
  2. UnicodeToLetter(10003) → cmark
  3. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
  4. TableText({rbDisplay}) → rbLabels
  5. LaTeX(If[a ≟ 1, If[currBaseIndx < 3, (("y=\left(" * Element[rbDisplay, currBaseIndx]) * "\right)^x"), (("y= \vphantom{\dfrac{1}{1}^2}" * Element[rbDisplay, currBaseIndx]) * "^x")], (((("y= \vphantom{\dfrac{1}{1}^2}" * a) * "\left(") * Element[rbDisplay, currBaseIndx]) * "\right)^x")]) → eqnDisp
  6. LaTeX("The graph below depicts a portion of the curve \(y=a\cdot c^x\).\\What do you notice about the \(x\)- and \(y\)-intercepts of the graph?") → MainInstruc
  7. LaTeX("Adjust the values of \(a\) and \(c\) and observe the resulting graph.") → SpecInstruc
  8. Intersect(f, yAxis, (0, 1)) → yIntercept
  9. Sequence((11.5 + i, 4.5), i, 1, 4) → rbPoints
  10. Element(rbPoints, 1) → rb1
  11. Element(rbPoints, 2) → rb2
  12. Element(rbPoints, 3) → rb3
  13. Element(rbPoints, 4) → rb4
  14. Element(rbPoints, currBaseIndx) → currBase
  15. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc
  16. Segment(legendAnchor, legendAnchor + (1.5, 0)) → legendF