函数的定义域与值域 by Breck Jacobs
几何画板及绘图内容加载中,请稍等……
①本范例演示了如何通过 GeoGebra 绘制函数的定义域与值域图形;②涉及的核心数学概念包括函数、定义域、值域、几何作图;③作图要点——从下方『构造摘要』提炼用到了 If, Min, Max, Intersect, Vector, Defined, Segment, IndexOf, Polygon 等GeoGebra命令/对象;④适合高中数学教学或自学,用于理解函数图像与性质。
GeoGebra 命令及参数
If(a, L, If[b, (1.5, 0), If[c, (1, 0)]]) → L1If(a, g1, If[b, g2, If[c, g3]]) → fMin(f, x(L1), rght) → mi11If(b, (0, 0), If[c, (0.5, 0), If[a, R]]) → R1Min(f, lft, x(R1)) → mig1Min(list2) → min_fMax(f, lft, x(R1)) → mag2Min(f, x(mag2), x(R1)) → mi_2Min(y(mi_2), x(mi11)) → MiEIntersect(f, j, x(mag2), x(mi_2)) → EIntersect(d, xAxis) → CIntersect(f, d, (-3, -1.7999999999999998)) → AVector(A, B) → uDefined(A) → eIf(x(L1) ≤ x1, If[x1 < x(R), B, R], L1) → end2Segment(L1, end2) → hIf(lft ≤ x1, If[x1 < x(R1), B, R1], L) → end1Segment(L, end1) → gIntersect(f, j, lft, x(mag2)) → DVector((x(L), f(x(L))), L) → vVector((x(R), f(x(R))), R) → wVector((x(L1), f(x(L1))), L1) → zVector((x(R1), f(x(R1))), R1) → lMax(f, x(L1), rght) → mag22Max(list1) → max_fVector((min_f, f(min_f)), (0, f(min_f))) → rIf(min_f ≤ y1, If[y1 < y(mag2), M, (0, y(mag2))], Y_l) → endv1Segment(Y_l, endv1) → tVector(D, (0, y(D))) → nIndexOf(max_f, list1) → Ind_maIndexOf(min_f, list2) → Ind_miVector(MiPt, (0, y(MiPt))) → v_1Vector(MaPt, (0, y(MaPt))) → u_1If(L1 ≠ L, Intersect[f, j, x(L1), rght], Intersect[f, j, x(mi_2), rght]) → FVector(E, (0, y(E))) → pVector(F, (0, y(F))) → qIf(min_f ≤ y1, If[y1 < y(mag2), (0, y(E)), (0, y(mag2))], (0, MiE)) → endv2Segment((0, MiE), endv2) → a_1If(min_f ≤ y1, If[y1 < y(mag22), (0, y(F)), (0, y(mag22))], (0, f(L1))) → endv3Segment((0, y(L1)), endv3) → b_1Segment((0, f(L1)), endv3) → c_1Polygon(Corner[1], (x(Corner[1]) + (0.3 * Distance[Corner[1], Corner[2]]), y(Corner[1])), (x(Corner[4]) + (0.3 * Distance[Corner[1], Corner[2]]), y(Corner[4])), Corner[4]) → poly1, d_1, e_1, f_1, g_1
AI 绘图提示语参考
绘制一个函数的图像,并标出其定义域和值域。首先绘制函数图像,然后使用条件语句确定定义域的边界点L1和R1,接着找到函数在这些边界点的值,用这些值构造水平线段表示值域。最后,通过条件语句和向量构造定义域和值域的边界线段,以及定义域和值域的交点。
以上提示语为根据原始绘图命令整理而来,仅供参考。