📚 IGCSE Mathematics: Transformations of Graphs (Translations) | IGCSE数学：函数图像的平移变换
In the IGCSE Edexcel Mathematics syllabus, transformations of graphs are a key topic. You are expected to recognise and describe translations, reflections, and stretches or compressions. This article focuses on translations: moving a graph horizontally, vertically, or both, without changing its shape, size, or orientation.
在 Edexcel IGCSE 数学考纲中，函数图像变换是一个重要考点。你需要能够识别并描述平移、反射和伸缩变换。本篇文章集中讲解平移变换：使图像在水平方向、竖直方向或同时两个方向上移动，而不改变其形状、大小和方向。
1. Understanding Translations and Vector Notation | 理解平移与向量记号
A translation slides every point on a graph by the same amount. If a point (x, y) is translated by the vector (a, b), its image is (x + a, y + b). The vector (a, b) means ‘a units horizontally and b units vertically’. A positive a moves right, a negative a moves left; a positive b moves up, a negative b moves down.
平移将图像上的每个点沿相同方向移动相同距离。若点 (x, y) 按向量 (a, b) 平移，则像点为 (x + a, y + b)。向量 (a, b) 表示“向右 a 个单位、向上 b 个单位”。a 为正向右，a 为负向左；b 为正向上，b 为负向下。
(x, y) → (x + a, y + b)
| Translation Vector | Direction |
|---|---|
| (3, 0) | 3 units right |
| (-2, 0) | 2 units left |
| (0, -4) | 4 units down |
| (-1, 5) | 1 unit left and 5 units up |
2. Vertical Translations: y
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