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函数图像的域与值域确定

函数图像的域与值域确定
几何画板及绘图内容加载中，请稍等……
2015-09-25 23:18
函数解析几何函数图像
所属专题 CCSS Support Math II Unit 2
①本范例演示如何通过 GeoGebra 绘制函数图像并确定其定义域和值域；②涉及的核心数学概念包括函数图像、定义域、值域、解析几何；③作图要点提炼自构造摘要，使用了 LaTeX、线段、多边形、交点等 GeoGebra 命令和对象；④适合高中数学教学，用于函数图像分析及域值域计算教学。

GeoGebra 命令及参数

  1. LaTeX("\text{Determine the domain and range of the following graph. }") → QuestionText
  2. LaTeX("\text{Determine the domain of the function.}") → text2
  3. LaTeX("\text{Determine the range of the function.") → text9
  4. LaTeX("\text{The domain is the set of \textcolor{#000099}{x}-values that are valid for the function. }") → text3
  5. LaTeX("\text{domain because the function is only valid when \textcolor{#000099}{x} is greater than or }") → text6
  6. LaTeX("\text{The range is the set of \textcolor{#000099}{y}-values that are valid for the function. ") → text10
  7. Segment(A, B) → a
  8. Segment(C, D) → b
  9. LaTeX((("\text{Domain=" * Constant) * "}")) → text15
  10. LaTeX((("\text{Range=" * sqrtx) * "}")) → text16
  11. LaTeX("\text{f(x)=\sqrt{x}}") → text14
  12. LaTeX("\text{f(x)=\sqrt{x}}") → FunctionText
  13. LaTeX("\text{x}") → text20
  14. LaTeX("\text{y}") → text21
  15. Segment(F, G) → c
  16. LaTeX((("\text{In this graph, the \textcolor{#000099}{y}-values start at \textcolor{#000099}{ y = " * sqrtx) * "} and continue to increase. ")) → text11
  17. Polygon(H, I, K, J) → poly1, h, i, k, j
  18. Intersect(h, i) → N
  19. Intersect(k, j) → O
  20. Polygon(L, M, N, O, R, S) → poly2, l, m, n, o, r, s
  21. LaTeX((("\text{The graph starts at \textcolor{#000099}{x = " * Constant) * "}, and continues infinitely in a positive}")) → text4
  22. LaTeX("\text{ direction. This means that only positive \textcolor{#000099}{x}-values are included in the") → text5
  23. LaTeX("\text{\mathbf{domain} the set of all input values (\textcolor{#000099}{x}-values) that satisfy the given function without}") → text1
  24. LaTeX("\text{restriction}") → text17
  25. LaTeX("\text{\mathbf{range} the set of all outputs of a function; the set of \textcolor{#000099}{y}-values that are valid for the}") → text18
  26. LaTeX("\text{function}") → text19
  27. LaTeX((("\text{equal to \textcolor{#000099}{" * Constant) * "}. }")) → text7
  28. LaTeX((("\text{Therefore, the domain is \textcolor{#000099}{\left\{ x ≥ " * Constant) * " \right\}}. }")) → text8
  29. LaTeX((("\text{Therefore, the range is all the numbers greater than or equal to \textcolor{#000099}{" * sqrtx) * "}.")) → text12
  30. LaTeX((("\text{The range is \textcolor{#000099}{\left\{ y ≥ " * sqrtx) * " \right\}}. }")) → text13