Answer:
Rotation can be represented as functions differently, depending on the rotation, we can define the common three based on rotations of 90° and 180°, clockwise or counterclockwise.
Rotation Rule for 90 Degrees Clockwise: (x, y) —> (y, -x)
Rotation Rule for 90 Degrees Counterclockwise: (x, y) —> (-y, x)
Rotation Rule for 180 Degrees: (x, y) —> (-x, -y)
All these rotations are made around the origin.
These rotations above are represented as a function, that is, an application between to sets. For example, to make a rotation of 90 degrees clockwise around the origin, we have to invert horizontal coordinates and vertical coordinates. In other words, we have to change the variables, each x-value will be now a y-value, additionally, each new y-value will be opposite, thats' what means (x, y) —> (y, -x).
So, basically, rotations as functions are transformations of a relation between to sets to another relation, where this last relation would be different, according to the rotation.