📚 Reciprocal Function Graphs: Asymptotes and Properties | 倒数函数图像：渐近线与性质
mptotes and shape of y = 1/x is essential for sketching more complex rational expressions.
倒数函数是 Edexcel A-Level 数学的核心内容。它们出现在坐标几何、有理函数，甚至微积分中，例如对 x⁻¹ 求导或积分 1/x。牢固理解 y = 1/x 的渐近线和形状，对于绘制更复杂的有理表达式图像至关重要。
1. What is a Reciprocal Function? | 什么是倒数函数？
made up of two separate branches: one in the first quadrant and one in the third quadrant.
标准倒数函数定义为 f(x) = 1/x，其中 x 为实数且 x ≠ 0。它通常也写作 y = x⁻¹。图像是一条由两条独立分支组成的双曲线：一条在第一象限，另一条在第三象限。
eans that as one variable becomes very large, the other becomes very small, and vice versa.
由于分子是常数，x × f(x) 始终等于 1。这意味着当一个变量变得很大时，另一个变量会变得很小，反之亦然。
2. The Graph of y = 1/x | y = 1/x 的图像
For x > 0, as x increases, f(x) decreases steadily toward 0. For x < 0, as x decreases, f(x) also moves toward 0 from below. The curve never touches either axis, because neither x nor y can ever be zero.
当 x > 0 时，随着 x 增大，f(x) 逐步减小并趋近于 0。当 x < 0 时，随着 x 减小，f(x) 同样从下方趋近于 0。曲线永远不会接触坐标轴，因为 x 和 y 都不可能为零。
The following table shows some values for the first quadrant branch.
下表显示了第一象限分支的一些取值。
| x | 0.5 | 1 | 2 | 4 |
| y = 1/x | 2 | 1 | 0.5 | 0.25 |
This clearly shows the decreasing trend. In the third quadrant, the values are symmetric in magnitude but negative.
这清楚展示了递减趋势。在第三象限中，数值在大小上对称，但符号为负。
3. Vertical Asymptote | 垂直渐近线
aph approaches but never crosses or touches. For y = 1/x, the vertical asymptote is x = 0.
垂直渐近线是一条图像趋近但永不跨越或接触的竖直直线。对于 y = 1/x，垂直渐近线是 x = 0。
As x approaches 0 from the right, y
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