What is the difference between an image and a pre-image in a transformation? how do you tell them apart?

The image is the result of performing a transformation, and the preimage is the original that you perform the transformation.

To tell them apart, they will usually be defined separately. For example, the square ABCD, when translated four units right becomes square A'B'C'D'.

If you know the transformation performed, you can apply this to differentiate between the preimage and image if they are not labeled. Only one square will be on the right of the other square, and since the translation is "four units right", it has to be the rightmost square that is the image.

All you have to do is multiply