积极 AI Logo 积极 AI

绝对值函数的平移变换

绝对值函数的平移变换
几何画板及绘图内容加载中，请稍等……
2019-03-05 02:01
函数变换函数图像
本范例演示了绝对值函数的平移变换。核心数学概念包括函数变换、平移。通过GeoGebra命令如Sequence、If、Textfield等构造，用户可以直观地观察函数图像的变化。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. UnicodeToLetter(8226) → bullet
  2. Random(-3, 3) → cVal
  3. Random(1, 10) → aValIndx
  4. Element(aValOptions, aValIndx) → aVal
  5. Sequence((12, i), i, 21, 0, -3.8) → boxAnchorRight
  6. UnicodeToLetter(10007) → xmark
  7. UnicodeToLetter(10003) → cmark
  8. If(F11, (("\textcolor{#1B5E20}{" * cmark) * "}"), (("\textcolor{#d32f2f}{" * xmark) * "}")) → G11
  9. If(F12, (("\textcolor{#1B5E20}{" * cmark) * "}"), (("\textcolor{#d32f2f}{" * xmark) * "}")) → G12
  10. If(F13, (("\textcolor{#1B5E20}{" * cmark) * "}"), (("\textcolor{#d32f2f}{" * xmark) * "}")) → G13
  11. If(F14, (("\textcolor{#1B5E20}{" * cmark) * "}"), (("\textcolor{#d32f2f}{" * xmark) * "}")) → G14
  12. If(F15, correct, incorrect) → G15
  13. If(F16, correct, incorrect) → G16
  14. LaTeX("\text{Vertical translation\hphantom{00000000} by a factor of }") → E14
  15. LaTeX("\text{Horizontal translation\hphantom{00000000} by a factor of }") → E13
  16. LaTeX("\text{Vertical\hphantom{00000000000000} by a factor of }") → E12
  17. LaTeX("\text{Reflection in the \(x\)-axis?}") → E15
  18. LaTeX("\text{Horizontal stretch?}") → E11
  19. LaTeX("\text{Reflection in the \(y\)-axis?}") → E16
  20. LaTeX(Expand[f]) → fTxt
  21. Textfield(F4) → E4
  22. Textfield(F5) → E5
  23. Textfield(F6) → E6
  24. Textfield(F7) → E7
  25. Sequence("\phantom{\dfrac{1}{2}vertical compression000000000}", i, 1, 6) → spacersDropDown
  26. LaTeX(If[aVal < 0, (bullet * " Reflection in the \(x\)-axis. \\"), ""]) → fbReflection
  27. LaTeX(If[abs(aVal) ≟ 1, "", If[abs(aVal) > 1, (((bullet * " Vertical stretch by a factor of ") * abs(aVal)) * ". \\"), (((bullet * " Vertical compression by a factor of ") * abs(1 / aVal)) * ". \\")]]) → fbvStretch
  28. LaTeX(If[abs(cVal) ≟ 0, "", (((((((bullet * " Horizontal translation ") * If[cVal < 0, "left", "right"]) * " by ") * abs(cVal)) * " unit") * If[abs(cVal) > 1, "s", ""]) * ".\\")]) → fbhTrans
  29. LaTeX(If[abs(dVal) ≟ 0, "", (((((((bullet * " Vertical translation ") * If[dVal < 0, "down", "up"]) * " by ") * abs(dVal)) * " unit") * If[abs(dVal) > 1, "s", ""]) * ".\\")]) → fbvTrans
  30. If(B6, If[SelectedIndex[hShiftLst] ≟ 1, G6, If[SelectedIndex[hShiftLst] ≟ 2, (-G6), 1]], 0) → userC
  31. If(B7, If[SelectedIndex[vShiftLst] ≟ 1, G7, If[SelectedIndex[vShiftLst] ≟ 2, (-G7), 1]], 0) → userD
  32. Polygon({(left, top), (right, top), (right, bottom), (left, bottom)}) → viewbox
  33. Segment(Element[legendAnchors, 1], Element[legendAnchors, 1] + (3, 0)) → legendF
  34. Segment(Element[legendAnchors, 2], Element[legendAnchors, 2] + (3, 0)) → legendH
  35. TableText({A2:A7, spacersDropDown, C2:C7}, "vr") → tblQuestions
  36. LaTeX(((((("\text{One possible solution is given below:\\" * fbReflection) * fbvStretch) * fbhTrans) * fbvTrans) * "}")) → fbComplete
  37. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc
  38. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewboxCover