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幂函数与几何图形

幂函数与几何图形
几何画板及绘图内容加载中，请稍等……
2022-07-03 15:14
函数微积分几何作图
本范例演示了幂函数的几何图形及其性质。通过输入不同的参数，可以观察到幂函数图像的变化。涉及的核心数学概念包括幂函数、实数和几何图形。使用了多项 GeoGebra 命令，如函数、图形、序列等。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Textfield(ax) → InputBox1
  2. Textfield(bx) → InputBox2
  3. Textfield(ay) → InputBox3
  4. Textfield(by) → InputBox4
  5. Textfield(b) → InputBox5
  6. Line(A4, xAxis) → i
  7. Line(A3, xAxis) → j
  8. Line(A2, yAxis) → k
  9. Line(A1, yAxis) → l
  10. Intersect(i, l) → A
  11. Intersect(i, k) → B
  12. Intersect(k, j) → C
  13. Intersect(l, j) → D
  14. Polygon(A, B, C, D) → poly1, s, t, d, e
  15. Segment(D', D) → m
  16. Segment(C', C) → n1
  17. Segment(B, B') → q
  18. Segment(A', A) → r
  19. Function(b, ax, bx, ay, by) → o
  20. Surface(ax, s, (t * o(ax, s)), s, ay, by, t, 0, 1) → u1
  21. Surface(bx, s, (t * o(bx, s)), s, ay, by, t, 0, 1) → u2
  22. Surface(s, ay, (t * o(s, ay)), s, ax, bx, t, 0, 1) → u3
  23. Surface(s, by, (t * o(s, by)), s, ax, bx, t, 0, 1) → u4
  24. Integral(b, y) → u
  25. Sequence(ay + (i * (by - ay) / n), i, 0, n) → list1, {0, 0.002, 0.004, 0.006, 0.008, 0.01, 0.012, 0.014, 0.016, 0.018000000000000002, 0.02, 0.022, 0.024, 0.026000000000000002, 0.028, 0.03, 0.032, 0.034, 0.036000000000000004, 0.038, 0.04, 0.042, 0.044, 0.046, 0.048, 0.05, 0.052000000000000005, 0.054, 0.056, 0.058, 0.06, 0.062, 0.064, 0.066, 0.068, 0.07, 0.07200000000000001, 0.074, 0.076, 0.078, 0.08, 0.082, 0.084, 0.08600000000000001, 0.088, 0.09, 0.092, 0.094, 0.096, 0.098, 0.1, 0.10200000000000001, 0.10400000000000001, 0.106, 0.108, 0.11, 0.112, 0.114, 0.116, 0.11800000000000001, 0.12, 0.122, 0.124, 0.126, 0.128, 0.13, 0.132, 0.134, 0.136, 0.138, 0.14, 0.14200000000000002, 0.14400000000000002, 0.146, 0.148, 0.15, 0.152, 0.154, 0.156, 0.158, 0.16, 0.162, 0.164, 0.166, 0.168, 0.17, 0.17200000000000001, 0.17400000000000002, 0.176, 0.178, 0.18, 0.182, 0.184, 0.186, 0.188, 0.19, 0.192, 0.194, 0.196, 0.198, 0.2, 0.202, 0.20400000000000001, 0.20600000000000002, 0.20800000000000002, 0.21, 0.212, 0.214, 0.216, 0.218, 0.22, 0.222, 0.224, 0.226, 0.228, 0.23, 0.232, 0.234, 0.23600000000000002, 0.23800000000000002, 0.24, 0.242, 0.244, 0.246, 0.248, 0.25, 0.252, 0.254, 0.256, 0.258, 0.26, 0.262, 0.264, 0.266, 0.268, 0.27, 0.272, 0.274, 0.276, 0.278, 0.28, 0.28200000000000003, 0.28400000000000003, 0.28600000000000003, 0.28800000000000003, 0.29, 0.292, 0.294, 0.296, 0.298, 0.3, 0.302, 0.304, 0.306, 0.308, 0.31, 0.312, 0.314, 0.316, 0.318, 0.32, 0.322, 0.324, 0.326, 0.328, 0.33, 0.332, 0.334, 0.336, 0.338, 0.34, 0.342, 0.34400000000000003, 0.34600000000000003, 0.34800000000000003, 0.35000000000000003, 0.352, 0.354, 0.356, 0.358, 0.36, 0.362, 0.364, 0.366, 0.368, 0.37, 0.372, 0.374, 0.376, 0.378, 0.38, 0.382, 0.384, 0.386, 0.388, 0.39, 0.392, 0.394, 0.396, 0.398, 0.4, 0.402, 0.404, 0.406, 0.40800000000000003, 0.41000000000000003, 0.41200000000000003, 0.41400000000000003, 0.41600000000000004, 0.418, 0.42, 0.422, 0.424, 0.426, 0.428, 0.43, 0.432, 0.434, 0.436, 0.438, 0.44, 0.442, 0.444, 0.446, 0.448, 0.45, 0.452, 0.454, 0.456, 0.458, 0.46, 0.462, 0.464, 0.466, 0.468, 0.47000000000000003, 0.47200000000000003, 0.47400000000000003, 0.47600000000000003, 0.47800000000000004, 0.48, 0.482, 0.484, 0.486, 0.488, 0.49, 0.492, 0.494, 0.496, 0.498, 0.5, 0.502, 0.504, 0.506, 0.508, 0.51, 0.512, 0.514, 0.516, 0.518, 0.52, 0.522, 0.524, 0.526, 0.528, 0.53, 0.532, 0.534, 0.536, 0.538, 0.54, 0.542, 0.544, 0.546, 0.548, 0.55, 0.552, 0.554, 0.556, 0.558, 0.56, 0.562, 0.5640000000000001, 0.5660000000000001, 0.5680000000000001, 0.5700000000000001, 0.5720000000000001, 0.5740000000000001, 0.5760000000000001, 0.578, 0.58, 0.582, 0.584, 0.586, 0.588, 0.59, 0.592, 0.594, 0.596, 0.598, 0.6, 0.602, 0.604, 0.606, 0.608, 0.61, 0.612, 0.614, 0.616, 0.618, 0.62, 0.622, 0.624, 0.626, 0.628, 0.63, 0.632, 0.634, 0.636, 0.638, 0.64, 0.642, 0.644, 0.646, 0.648, 0.65, 0.652, 0.654, 0.656, 0.658, 0.66, 0.662, 0.664, 0.666, 0.668, 0.67, 0.672, 0.674, 0.676, 0.678, 0.68, 0.682, 0.684, 0.686, 0.6880000000000001, 0.6900000000000001, 0.6920000000000001, 0.6940000000000001, 0.6960000000000001, 0.6980000000000001, 0.7000000000000001, 0.7020000000000001, 0.704, 0.706, 0.708, 0.71, 0.712, 0.714, 0.716, 0.718, 0.72, 0.722, 0.724, 0.726, 0.728, 0.73, 0.732, 0.734, 0.736, 0.738, 0.74, 0.742, 0.744, 0.746, 0.748, 0.75, 0.752, 0.754, 0.756, 0.758, 0.76, 0.762, 0.764, 0.766, 0.768, 0.77, 0.772, 0.774, 0.776, 0.778, 0.78, 0.782, 0.784, 0.786, 0.788, 0.79, 0.792, 0.794, 0.796, 0.798, 0.8, 0.802, 0.804, 0.806, 0.808, 0.81, 0.812, 0.8140000000000001, 0.8160000000000001, 0.8180000000000001, 0.8200000000000001, 0.8220000000000001, 0.8240000000000001, 0.8260000000000001, 0.8280000000000001, 0.8300000000000001, 0.8320000000000001, 0.834, 0.836, 0.838, 0.84, 0.842, 0.844, 0.846, 0.848, 0.85, 0.852, 0.854, 0.856, 0.858, 0.86, 0.862, 0.864, 0.866, 0.868, 0.87, 0.872, 0.874, 0.876, 0.878, 0.88, 0.882, 0.884, 0.886, 0.888, 0.89, 0.892, 0.894, 0.896, 0.898, 0.9, 0.902, 0.904, 0.906, 0.908, 0.91, 0.912, 0.914, 0.916, 0.918, 0.92, 0.922, 0.924, 0.926, 0.928, 0.93, 0.932, 0.934, 0.936, 0.9380000000000001, 0.9400000000000001, 0.9420000000000001, 0.9440000000000001, 0.9460000000000001, 0.9480000000000001, 0.9500000000000001, 0.9520000000000001, 0.9540000000000001, 0.9560000000000001, 0.9580000000000001, 0.96, 0.962, 0.964, 0.966, 0.968, 0.97, 0.972, 0.974, 0.976, 0.978, 0.98, 0.982, 0.984, 0.986, 0.988, 0.99, 0.992, 0.994, 0.996, 0.998, 1}
  26. Element(list3, faces) → Selectedvector

AI 绘图提示语参考

绘制一个展示幂函数几何形状和性质的图形。首先画出坐标轴，然后在轴上标出几个关键点，连接这些点形成一个四边形。接着，根据输入的参数绘制两条幂函数曲线，并生成它们的表面图。最后，在曲面上绘制一些等高线，以展示函数的变化趋势。
以上提示语为根据原始绘图命令整理而来，仅供参考。