Describe the Column of Trajan (above), including how it serves to both document and commemorate history.

relief sculpture - images are set against a flat background.

a coin is a good example: the inscription, the date, and the figure are slightly raised above a flat surface. the ancient egyptians sometimes carved figures into a flat surface.  

pro: they take significantly less time to make and do not require as much tools or skills as free-standing

cons: not nearly as realistic, as it is not fully 3-d, and does not have the details that a free-standing one does.

freestanding sculptures (also called  carved in the round) are not attached to any  background.   they are 3-dimensional  and fully rendered.