- Reflection is a more familiar transformation to us: we usually see our reflections in a mirror.
- In Cartesian plane, a line will be the ‘mirror’, and the function will be reflected along the ‘mirror’. Therefore, the line can be horizontal, vertical, or diagonal. Here, we will only consider horizontal and vertical reflection, as diagonal reflections are too complex for this course. In particular, we will only study reflections along the x-axis and y-axis.
- A reflection along the x-axis gives the following transformation:
(x,\ y) \rightarrow(x,\ -y)
and a reflection along the y-axis gives the following transformation: