GeoGebra数学范例:多函数与几何作图
几何画板及绘图内容加载中,请稍等……
所属专题
Function Arts
本范例通过GeoGebra演示多函数图像与几何作图关系。核心数学概念包括幂函数、三角函数、条件概率及微分学。作图要点涉及A、B、f、g、h等对象的构造,以及f₁、g₁等参数的调整。适合高中生学习函数图像变换与几何直观应用。
GeoGebra 命令及参数
(-5.872, 0.118)(6.1, 0.11)f(x) = ((x + 3) * 0.429) + 0.7g(x) = If[-3 ≤ x ≤ 6, f(x)]h(x) = (0.13 * (x + 4.5)^(2)) + 0.4p(x) = If[-4.5 ≤ x ≤ -3, h(x)]q(x) = (0.5 * (x + 4.5)^(2)) + 0.4r(x) = If[-5.6 ≤ x ≤ -4.5, q(x)]s(x) = (3.8 * (x + 5.4)^(2)) + 0.87f_{1}(x) = (4.9 * sin(x + 6.55)) - 1.7g_{1}(x) = If[-5.83 ≤ x ≤ -5.4, f_{1}(x)]h_{1}(x) = (1.5 * (x + 5.4)) + 2.8p_{1}(x) = If[-5.4 ≤ x ≤ -4.4, h_{1}(x)]q_{1}(x) = (3 * (x + 4.6)) + 3.6r_{1}(x) = If[-4.6 ≤ x ≤ -4.36, q_{1}(x)]s_{1}(x) = (19 * (x + 4.4)^(2)) + 2.7t_{1}(x) = If[-4.615 ≤ x ≤ -4.4, s_{1}(x)]f_{2}(x) = (0.49 * (x + 3.4)^(2)) + 2.2g_{2}(x) = If[-4.4 ≤ x ≤ -3.4, f_{2}(x)]h_{2}(x) = (0.268 * (x + 3)) + 2.2p_{2}(x) = If[-3 ≤ x ≤ 6, h_{2}(x)]q_{2}(x) = (0 * (x + 3.4)) + 2.2r_{2}(x) = If[-3.4 ≤ x ≤ -3, q_{2}(x)]s_{2}(x) = (2.6 * (x + 4.2)) + 3.4t(x) = If[-5.81 ≤ x ≤ -5.5, s(x)]f_{3}(x) = (2.6 * (x + 3.42)) + 3.4g_{3}(x) = If[-3.43 ≤ x ≤ -2.94, f_{3}(x)]h_{3}(x) = (0 * (x + 4.2)) + 3.38p_{3}(x) = If[-4.2 ≤ x ≤ -3.4, h_{3}(x)]q_{3}(x) = (0 * (x + 3)) + 6.54r_{3}(x) = If[-3 ≤ x ≤ -2.2, q_{3}(x)]s_{3}(x) = (16 * (x + 2.3)) + 5.1t_{3}(x) = If[-2.3 ≤ x ≤ -2.21, s_{3}(x)]f_{4}(x) = (16 * (x + 3)) + 3.4g_{4}(x) = If[-3 ≤ x ≤ -2.92, f_{4}(x)]h_{4}(x) = (0 * (x + 3)) + 3.4p_{4}(x) = If[-3 ≤ x ≤ -2.2, h_{4}(x)]q_{4}(x) = (2.8 * (x + 2.27)) + 5.1r_{4}(x) = If[-2.3 ≤ x ≤ -1.76, q_{4}(x)]s_{4}(x) = (2.6 * (x + 2.2)) + 3.4f_{5}(x) = (0 * (x + 1.8)) + 6.57g_{5}(x) = If[-1.76 ≤ x ≤ -1, f_{5}(x)]h_{5}(x) = (2.6 * (x + 2.1)) + 3.4p_{5}(x) = If[-2.1 ≤ x ≤ -0.9, h_{5}(x)]q_{5}(x) = (2.6 * (x + 1.38)) + 3.4r_{5}(x) = If[-1.38 ≤ x ≤ -0.18, q_{5}(x)]s_{5}(x) = (0 * (x + 1.2)) + 3.4t_{5}(x) = If[-2.1 ≤ x ≤ -1.4, s_{5}(x)]f_{6}(x) = (0 * (x + 0.9)) + 6.57h_{6}(x) = (2.7 * (x + 1.2)) + 3.4p_{6}(x) = If[-1.2 ≤ x ≤ -0.05, h_{6}(x)]g_{6}(x) = If[-0.9 ≤ x ≤ -0.16, f_{6}(x)]q_{6}(x) = (2.6 * (x + 0.45)) + 3.4r_{6}(x) = If[-0.45 ≤ x ≤ 0.04, q_{6}(x)]s_{6}(x) = (2.6 * (x - 04)) + 15t_{2}(x) = If[-4.2 ≤ x ≤ -3, s_{2}(x)]t_{6}(x) = If[0.4 ≤ x ≤ 0.75, s_{6}(x)]f_{7}(x) = (-24 * (x - 0.15)) + 3.3g_{7}(x) = If[0.09 ≤ x ≤ 0.147, f_{7}(x)]h_{7}(x) = (-22 * (x - 1))
AI 绘图提示语参考
绘制包含多个函数图像的图形,展示幂函数、三角函数与几何构造的关系。主要对象包括分段定义的函数 f、g、h 及其变形,以及基于条件概率的几何曲线。先画出基础函数曲线,再添加条件控制的几何对象,最后叠加三角函数图像,体现函数变换与几何直观。
以上提示语为根据原始绘图命令整理而来,仅供参考。