函数变换演示 by Luke Underwood

几何画板及绘图内容加载中，请稍等……

2016-03-22 11:31

①本范例演示了三角函数图像的平移、伸缩等变换效果；②涉及核心数学概念包括函数图像变换、振幅、周期、相位移动和垂直平移；③作图要点提炼自GeoGebra命令：使用Text, If, Max, fChoice, vcp, a, b, c, d, amplitude, period, phaseshift, verticalshift, yMin, yox, xoy, yMax, xMin, trigxChoice, xMax, pieChoice, piText, piUnit, trigxText, fxButton, fxtnButton, fnrxButton, fabsxButton, fooxButton, fntxButton, flnxButton, fsinButton, fcosButton, ftanButton, fcotButton, fcscButton, fsecButton, n, ftrigx, pie, nShow, FunctionButtons等；④适合高中数学教学，用于理解函数变换规律和应用。

GeoGebra 命令及参数

Text("x") → fChoice
If(fChoice ≟ "fsin", "sin", If[fChoice ≟ "fcos", "cos", If[fChoice ≟ "ftan", "tan", If[fChoice ≟ "fsec", "sec", If[fChoice ≟ "fcsc", "csc", If[fChoice ≟ "fcot", "cot"]]]]]) → trigxChoice
If(pieChoice ≟ true, "π", "") → piText
If(pieChoice ≟ true, π, 1) → piUnit
If(fChoice ≟ "fsin" ∨ fChoice ≟ "fcos" ∨ fChoice ≟ "ftan" ∨ fChoice ≟ "fcot" ∨ fChoice ≟ "fcsc" ∨ fChoice ≟ "fsec", true, false) → ftrigx
If(pieChoice ≟ true ∧ ftrigx ≟ true, true, false) → pie
If(fChoice ≟ "fxtn" ∨ fChoice ≟ "fnrx" ∨ fChoice ≟ "fntx" ∨ fChoice ≟ "flnx", true, false) → nShow
If(fChoice ≟ "fsin" ∧ pieChoice ≟ false, (a * sin((b * x) + c)) + d, If[fChoice ≟ "fcos" ∧ pieChoice ≟ false, (a * cos((b * x) + c)) + d, If[fChoice ≟ "fsin" ∧ pieChoice ≟ true, (a * sin(((b * π) * x) + (c * π))) + d, If[fChoice ≟ "fcos" ∧ pieChoice ≟ true, (a * cos(((b * π) * x) + (c * π))) + d, If[fChoice ≟ "ftan" ∧ pieChoice ≟ false, (a * tan((b * x) + c)) + d, If[fChoice ≟ "ftan" ∧ pieChoice ≟ true, (a * tan(((b * π) * x) + (c * π))) + d, If[fChoice ≟ "fcot" ∧ pieChoice ≟ false, (a * cot((b * x) + c)) + d, If[fChoice ≟ "fcot" ∧ pieChoice ≟ true, (a * cot(((b * π) * x) + (c * π))) + d, If[fChoice ≟ "fcsc" ∧ pieChoice ≟ false, (a * csc((b * x) + c)) + d, If[fChoice ≟ "fcsc" ∧ pieChoice ≟ true, (a * csc(((b * π) * x) + (c * π))) + d, If[fChoice ≟ "fsec" ∧ pieChoice ≟ false, (a * sec((b * x) + c)) + d, If[fChoice ≟ "fsec" ∧ pieChoice ≟ true, (a * sec(((b * π) * x) + (c * π))) + d, If[fChoice ≟ "fx", (a * ((b * x) + c)) + d, If[fChoice ≟ "fxtn", (a * ((b * x) + c)^(n)) + d, If[fChoice ≟ "fnrx", (a * ((b * x) + c)^(1 / n)) + d, If[fChoice ≟ "fabsx", (a * abs((b * x) + c)) + d, If[fChoice ≟ "foox", a / ((b * x) + c) + d, If[fChoice ≟ "fntx", (a * n^((b * x) + c)) + d, If[fChoice ≟ "flnx", (a * log(n, (b * x) + c)) + d, (a * ((b * x) + c)) + d]]]]]]]]]]]]]]]]]]) → f
If(fChoice ≟ "fx", fxText, If[fChoice ≟ "fxtn", fxtnText, If[fChoice ≟ "fnrx", fnrxText, If[fChoice ≟ "fabsx", fabsxText, If[fChoice ≟ "foox", fooxText, If[fChoice ≟ "fntx", fntxText, If[fChoice ≟ "flnx", flnxText, If[Defined[trigxChoice], trigxText, fxText]]]]]]]) → FunctionText
If(fChoice ≟ "fx", fxTextB, If[fChoice ≟ "fxtn", fxtnTextB, If[fChoice ≟ "fnrx", fnrxTextB, If[fChoice ≟ "fabsx", fabsxTextB, If[fChoice ≟ "foox", fooxTextB, If[fChoice ≟ "fntx", fntxTextB, If[fChoice ≟ "flnx", flnxTextB, If[Defined[trigxChoice], trigxTextB, fxTextB]]]]]]]) → FunctionTextB
If(fChoice ≟ "fx", x, If[fChoice ≟ "fxtn", x^(n), If[fChoice ≟ "fnrx", x^(1 / n), If[fChoice ≟ "fabsx", abs(x), If[fChoice ≟ "foox", 1 / x, If[fChoice ≟ "fntx", n^(x), If[fChoice ≟ "flnx", log(n, x), If[fChoice ≟ "fsin", sin(x), If[fChoice ≟ "fcos", cos(x), If[fChoice ≟ "ftan", tan(x), If[fChoice ≟ "fcsc", csc(x), If[fChoice ≟ "fsec", sec(x), If[fChoice ≟ "fcot", cot(x)]]]]]]]]]]]]) → P

AI 绘图提示语参考

绘制一个展示三角函数图像变换的图形，包括正弦、余弦、正切等函数的平移、伸缩、振幅调整、周期变化、相位偏移和垂直平移。通过不同参数的调整，展示函数图像如何变化，并标注关键概念如振幅、周期、相位偏移和垂直平移，适合高中数学教育。

以上提示语为根据原始绘图命令整理而来，仅供参考。