Transforming Functions | 函数图像变换

📚 Transforming Functions | 函数图像变换

Transforming functions means applying a set of rules to move, stretch, compress or reflect the graph of y = f(x). These transformations appear throughout Edexcel A Level Pure Mathematics and are often tested by sketching graphs, finding new equations or working out the image of a point.

函数图像变换指的是对 y = f(x) 的图像进行平移、伸缩、压缩或对称反射。这些内容是 Edexcel A Level 纯数学的核心考点，常见题型包括画图、求变换后的函数表达式以及求某点变换后的坐标。

1. Core Transformation Rules | 核心变换规则

The graph of y = f(x) can be transformed by changing the equation on the outside or the inside of the function bracket.

函数图像可以通过改变函数符号外部或内部的表达式来实现变换。

Outside changes affect y-coordinates directly, while inside changes affect x-coordinates and often work in the reverse direction.

函数外部的变化直接影响 y 坐标，而内部的变化影响 x 坐标，并且作用方向常常相反。

The table below summarises the six standard transformations for y = f(x).

下表总结了 y = f(x) 的六种标准变换形式。