积极 AI Logo 积极 AI

对数函数与时间的关系

对数函数与时间的关系
几何画板及绘图内容加载中，请稍等……
2022-01-30 18:27
函数立体几何微积分极限函数图像
①本范例通过动态演示对数函数图像，展示其随时间变化的规律；②涉及核心数学概念包括对数函数、极限、立体几何中的几何体、百分比计算；③作图要点使用了GeoGebra的Sequence（数列）、Point（点）、Segment（线段）等命令，构建函数图像与几何体；④适合高中及以上数学学习者，用于理解对数函数的应用与可视化。

GeoGebra 命令及参数

  1. Sequence(Segment[(k, 0), (k, 0.5)], k, -10, 10) → l1, {0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5}
  2. Sequence((log(10, k), 0), k, 1, 9) → l2, {(0, 0), (0.30102999566398114, 0), (0.47712125471966244, 0), (0.6020599913279623, 0), (0.6989700043360187, 0), (0.7781512503836435, 0), (0.8450980400142567, 0), (0.9030899869919434, 0), (0.9542425094393249, 0)}
  3. Sequence(Translate[l2, Vector[(0, 0), (k, 0)]], k, -10, 9) → m1, {{(-10, 0), (-9.698970004336019, 0), (-9.522878745280337, 0), (-9.397940008672037, 0), (-9.301029995663981, 0), (-9.221848749616356, 0), (-9.154901959985743, 0), (-9.096910013008056, 0), (-9.045757490560675, 0)}, {(-9, 0), (-8.698970004336019, 0), (-8.522878745280337, 0), (-8.397940008672037, 0), (-8.301029995663981, 0), (-8.221848749616356, 0), (-8.154901959985743, 0), (-8.096910013008056, 0), (-8.045757490560675, 0)}, {(-8, 0), (-7.698970004336019, 0), (-7.522878745280337, 0), (-7.3979400086720375, 0), (-7.301029995663981, 0), (-7.221848749616356, 0), (-7.154901959985743, 0), (-7.096910013008056, 0), (-7.045757490560675, 0)}, {(-7, 0), (-6.698970004336019, 0), (-6.522878745280337, 0), (-6.3979400086720375, 0), (-6.301029995663981, 0), (-6.221848749616356, 0), (-6.154901959985743, 0), (-6.096910013008056, 0), (-6.045757490560675, 0)}, {(-6, 0), (-5.698970004336019, 0), (-5.522878745280337, 0), (-5.3979400086720375, 0), (-5.301029995663981, 0), (-5.221848749616356, 0), (-5.154901959985743, 0), (-5.096910013008056, 0), (-5.045757490560675, 0)}, {(-5, 0), (-4.698970004336019, 0), (-4.522878745280337, 0), (-4.3979400086720375, 0), (-4.301029995663981, 0), (-4.221848749616356, 0), (-4.154901959985743, 0), (-4.096910013008056, 0), (-4.045757490560675, 0)}, {(-4, 0), (-3.6989700043360187, 0), (-3.5228787452803374, 0), (-3.3979400086720375, 0), (-3.3010299956639813, 0), (-3.2218487496163566, 0), (-3.154901959985743, 0), (-3.0969100130080567, 0), (-3.0457574905606752, 0)}, {(-3, 0), (-2.6989700043360187, 0), (-2.5228787452803374, 0), (-2.3979400086720375, 0), (-2.3010299956639813, 0), (-2.2218487496163566, 0), (-2.154901959985743, 0), (-2.0969100130080567, 0), (-2.0457574905606752, 0)}, {(-2, 0), (-1.6989700043360187, 0), (-1.5228787452803376, 0), (-1.3979400086720377, 0), (-1.3010299956639813, 0), (-1.2218487496163566, 0), (-1.1549019599857433, 0), (-1.0969100130080567, 0), (-1.0457574905606752, 0)}, {(-1, 0), (-0.6989700043360189, 0), (-0.5228787452803376, 0), (-0.3979400086720377, 0), (-0.30102999566398125, 0), (-0.22184874961635648, 0), (-0.1549019599857433, 0), (-0.09691001300805657, 0), (-0.04575749056067513, 0)}, {(0, 0), (0.30102999566398114, 0), (0.47712125471966244, 0), (0.6020599913279623, 0), (0.6989700043360187, 0), (0.7781512503836435, 0), (0.8450980400142567, 0), (0.9030899869919434, 0), (0.9542425094393249, 0)}, {(1, 0), (1.3010299956639813, 0), (1.4771212547196624, 0), (1.6020599913279623, 0), (1.6989700043360187, 0), (1.7781512503836434, 0), (1.8450980400142567, 0), (1.9030899869919433, 0), (1.9542425094393248, 0)}, {(2, 0), (2.3010299956639813, 0), (2.4771212547196626, 0), (2.6020599913279625, 0), (2.6989700043360187, 0), (2.7781512503836434, 0), (2.845098040014257, 0), (2.9030899869919433, 0), (2.9542425094393248, 0)}, {(3, 0), (3.3010299956639813, 0), (3.4771212547196626, 0), (3.6020599913279625, 0), (3.6989700043360187, 0), (3.7781512503836434, 0), (3.845098040014257, 0), (3.9030899869919433, 0), (3.9542425094393248, 0)}, {(4, 0), (4.301029995663981, 0), (4.477121254719663, 0), (4.6020599913279625, 0), (4.698970004336019, 0), (4.778151250383644, 0), (4.845098040014257, 0), (4.903089986991944, 0), (4.954242509439325, 0)}, {(5, 0), (5.301029995663981, 0), (5.477121254719663, 0), (5.6020599913279625, 0), (5.698970004336019, 0), (5.778151250383644, 0), (5.845098040014257, 0), (5.903089986991944, 0), (5.954242509439325, 0)}, {(6, 0), (6.301029995663981, 0), (6.477121254719663, 0), (6.6020599913279625, 0), (6.698970004336019, 0), (6.778151250383644, 0), (6.845098040014257, 0), (6.903089986991944, 0), (6.954242509439325, 0)}, {(7, 0), (7.301029995663981, 0), (7.477121254719663, 0), (7.6020599913279625, 0), (7.698970004336019, 0), (7.778151250383644, 0), (7.845098040014257, 0), (7.903089986991944, 0), (7.954242509439325, 0)}, {(8, 0), (8.301029995663981, 0), (8.477121254719663, 0), (8.602059991327963, 0), (8.698970004336019, 0), (8.778151250383644, 0), (8.845098040014257, 0), (8.903089986991944, 0), (8.954242509439325, 0)}, {(9, 0), (9.301029995663981, 0), (9.477121254719663, 0), (9.602059991327963, 0), (9.698970004336019, 0), (9.778151250383644, 0), (9.845098040014257, 0), (9.903089986991944, 0), (9.954242509439325, 0)}}
  4. Point(m1) → P1
  5. Segment(Q1, R1) → i1
  6. Segment(R1, S1) → j1
  7. Sequence(Segment[(log(10, k), 0), (log(10, k), 0.4)], k, 2, 9) → l3, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}
  8. Sequence(Translate[l3, Vector[(0, 0), (k, 0)]], k, -10, 9) → m2, {{0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}, {0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4, 0.4}}
  9. Segment((x(P1), -2), (x(P1), 2)) → h1'
  10. Point(h1') → P1'
  11. Segment((x(P1), -0.5), (x(P1), 0.8)) → h1
  12. Point(m1) → P2
  13. Segment((x(P2), -0.5), (x(P2), 0.8)) → h2
  14. Segment((x(P2), -2), (x(P2), 2)) → h2'
  15. Segment(Q2, R2) → i2
  16. Segment(R2, S2) → j2
  17. Point(h2') → P2'
  18. Point(m1) → P3
  19. Segment((x(P3), -0.5), (x(P3), 0.8)) → h3
  20. Segment((x(P3), -2), (x(P3), 2)) → h3'
  21. Point(h3') → P3'
  22. Segment(Q3, R3) → i3
  23. Segment(R3, S3) → j3
  24. Point(g) → P4
  25. Segment((x(P4), -0.5), (x(P4), 0.8)) → h4
  26. Segment(Q4, R4) → i4
  27. Segment(R4, S4) → j4

AI 绘图提示语参考

绘制一个对数函数图像，从-10到10的x轴上，每隔一个单位向上移动0.5个单位画一条水平线段。然后，以对数函数y=log10(x)的形式，从1到9的x值绘制一系列点，并将这些点沿x轴平移，形成一系列平行于x轴的线段。接着，画出x轴上-2到2的垂直线段，并在每个点上标记。最后，画出从这些点出发的水平线段，形成一个类似梯形的图形。
以上提示语为根据原始绘图命令整理而来，仅供参考。