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IM Alg1.1.9 Practice: Technological Graphing

IM Alg1.1.9 Practice: Technological Graphing
几何画板及绘图内容加载中，请稍等……
2020-11-14 20:16
函数解析几何变换滑块动画函数图像
① This example demonstrates how to use GeoGebra's interactive input boxes and buttons to dynamically plot function graphs and observe the effects of parameter changes on the graphical representation. ② Core mathematical concepts include points on the coordinate plane, function graphs, slope and difference, dilation, and three-dimensional vectors (as background context), along with arithmetic operations and conditional logic. ③ Construction highlights: from the construction summary, commands such as Corner, Textfield, Polygon, and If are used; multiple coordinate range variables (xmin, xmax, ymin, ymax) and function-related objects (fx, fy) are created, with InputBox1-4 providing interactive input, buttons (button1, button2) triggering actions, and numerous auxiliary objects (a1-a18) controlling display and calculations. ④ Suitable for upper middle school or high school algebra courses, as a technology-assisted graphing practice to help students understand function transformations and coordinate geometry while developing skills with dynamic mathematics software.

GeoGebra 命令及参数

  1. Corner(1) → c1
  2. Corner(3) → c3
  3. Textfield(xxmin) → InputBox1
  4. Textfield(xxmax) → InputBox2
  5. Textfield(yymax) → InputBox4
  6. Textfield(yymin) → InputBox3
  7. Polygon(B1, A1, A2, C2) → q1, b1, f, g, c2
  8. Polygon(B2, A2, A3, C3) → q2, b2, h, i, l
  9. Polygon(B3, A3, A4, C1) → q3, b3, m, n, p
  10. Polygon(B4, A4, A5, C5) → q4, b4, q, r, c5
  11. Polygon(B5, C6, A6, A5) → q5, b5, c6, s, t
  12. Polygon(B6, C7, A7, A6) → q6, b6, c7, a, c
  13. Polygon(B7, C8, A8, A7) → q7, b7, c8, d, e
  14. Polygon(B8, C9, A9, A8) → q8, b8, c9, f_1, g_1
  15. Polygon(B9, C10, A10, A9) → q9, b9, c10, h_1, i_1
  16. Polygon(B10, C11, A11, A10) → q10, b10, c11, j_1, k_1
  17. Polygon(B11, C12, A12, A11) → q11, b11, c12, l_1, m_1
  18. Polygon(B12, C13, A13, A12) → q12, b12, c13, n_1, p_1
  19. Polygon(B13, C14, A14, A13) → q13, b13, c14, q_1, r_1
  20. Polygon(B14, C15, A15, A14) → q14, b14, c15, s_1, t_1
  21. Polygon(B15, C16, A16, A15) → q15, b15, c16, a_1, b_1
  22. Polygon(B16, C17, A17, A16) → q16, b16, c17, c_1, d_1
  23. Polygon(B17, C18, A18, A17) → q17, b17, c18, e_1, f_2
  24. Polygon(B18, C19, A19, A18) → q18, b18, c19, g_2, h_2
  25. Polygon(B19, C20, A20, A19) → q19, b19, c20, i_2, j_2
  26. Polygon(B20, C21, A, A20) → q20, b20, c21, a_2, k_2
  27. Textfield(a1) → InputBox5
  28. Textfield(a2) → InputBox6
  29. Textfield(a3) → InputBox7
  30. Textfield(a4) → InputBox8
  31. Textfield(a5) → InputBox9
  32. Textfield(a6) → InputBox10
  33. Textfield(a7) → InputBox11
  34. Textfield(a8) → InputBox12
  35. Textfield(a9) → InputBox13
  36. Textfield(a10) → InputBox14
  37. Textfield(a11) → InputBox15
  38. Textfield(a12) → InputBox16
  39. Textfield(a13) → InputBox17
  40. Textfield(a14) → InputBox18
  41. Textfield(a15) → InputBox19
  42. Textfield(a16) → InputBox20
  43. Textfield(a17) → InputBox21
  44. Textfield(a18) → InputBox22
  45. Textfield(a19) → InputBox23
  46. Textfield(a20) → InputBox24
  47. If(SelectedIndex[list] < 20, 20, 22) → o
  48. If(SelectedIndex[list] < 20, 20, 22) → u
  49. If(SelectedIndex[list] < 20, 20, 22) → v
  50. If(SelectedIndex[list] < 20, 20, 22) → w

AI 绘图提示语参考

在坐标平面上建立一个动态的多边形分割图形：先放置四个可交互的边界输入框，用于设置左右的最小与最大范围以及上下的最小与最大范围。根据这些范围在平面内依次生成一串首尾相接的多边形块，使用多组顶点围成从左到右的连续带状区域，并在相邻块之间共享端点以保持拼接。随后再添加若干用于控制这些块参数的输入框，使其可随数值变化而调整每个多边形的位置与形状。最后加入一个基于当前选择索引的条件显示/切换效果，使图形在两种状态之间变化。
以上提示语为根据原始绘图命令整理而来，仅供参考。