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IF2-02-CYU3: Name the Translations

IF2-02-CYU3: Name the Translations
几何画板及绘图内容加载中，请稍等……
2019-02-14 03:14
函数微积分积分变换函数图像
This interactive GeoGebra example is designed to help students practice identifying horizontal and vertical translations of function graphs. It randomly generates a base function template, applies a horizontal shift h and a vertical shift k, and presents the resulting graph. Students must determine the direction of each translation (left, right, up, down) and name it correctly. The core mathematical concepts include function transformations, similarity transformations, and the effect of the constant of integration in indefinite integrals. The construction uses GeoGebra commands such as If, RandomElement, and LaTeX to create randomized questions, with boolean variables (e.g., isUpChosen, isLeftChosen) controlling the translation directions. Interactive elements like the TryAnother button generate new problems, and feedback mechanisms (correct/incorrect) check student responses. This resource is suitable for high school or introductory college courses in algebra, precalculus, or calculus, particularly for reinforcing the visual understanding of function shifts and the role of constants in integrals.

GeoGebra 命令及参数

  1. If(Random[0, 1] ≟ 0, Random[-10, -1], Random[1, 10]) → h
  2. If(Random[0, 1] ≟ 0, Random[-10, -1], Random[1, 10]) → k
  3. RandomElement({x^(2), sqrt(x), 1 / x}) → f
  4. LaTeX(f(x - h) + k, false) → templateFunction
  5. LaTeX(UnicodeToLetter[10007]) → xmark
  6. LaTeX(UnicodeToLetter[10003]) → cmark
  7. If(h > 1, "right", "left") → horDir
  8. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  9. LaTeX((("\text{Horizontal translation \textbf{left} by \(" * abs(h)) * "\) unit(s)}")) → leftText
  10. LaTeX((("\text{Horizontal translation \textbf{right} by \(" * abs(h)) * "\) unit(s)}")) → rightText
  11. LaTeX((("\text{Vertical translation \textbf{up} by \(" * abs(k)) * "\) unit(s)}")) → upText
  12. LaTeX((("\text{Vertical translation \textbf{down} by \(" * abs(k)) * "\) unit(s)}")) → downText
  13. If(k > 0, "up", "down") → verDir

AI 绘图提示语参考

画一个基础函数图像，然后将其水平向左或向右平移，再垂直向上或向下平移，展示出函数图像的平移变换。标注出水平平移的方向和距离，以及垂直平移的方向和距离，并用文字说明平移的方向和距离。
以上提示语为根据原始绘图命令整理而来，仅供参考。