If is a map
(a.k.a. function, transformation,
etc.) over a domain
, then the image of
, also called the range of
under
,
is defined as the set of all values that
can take as its argument varies over
, i.e.,
"Image" is a synonym for "range," but "image" is the term preferred in formal mathematical writing.
The notation
denotes the image of the interval
under the function
. Formally,