# symmetry-translation-function-linearity.mp4

Chapter section: Translations and Function Representation

Caption (verbatim):

A function representation is linear

Image description (verbatim):

Function translation preserving linearity

## Before the animation

Chapter lines 549–549:

The zero function is also fixed:

Chapter lines 551–553:

```math
T_a0=0.
```

## After the animation

Chapter lines 561–561:

This makes sense. Translational symmetry needs an object to translate, just as $D_3$ symmetry needs a triangly thing to translate. We can think of the function as a shape. If a system possesses translational symmetry, that shape is preserved.

Chapter lines 563–563:

This describes how the function transforms. Whether the physical system it describes behaves the same way after translation is a separate question.