The image of a mapping is the subset of the range which the mapping actually returns as output. For example, the Pet-Of mapping from humans to animals will have an subtype of animals that are pets at any given time, namely Pet, which is the image. Whereas the range gives the possible results of the mapping, the image gives the actual results. If the image is the same as the range, the mapping is said to be onto or surjective; otherwise it is called into or injective. Since mappings always return sets, to accommodate multiple-values and no-values, it is more exact to say that the image is the subset of the range which has the members in at least one of the sets returned by the mapping. There are three ways of modelling images: 1) Both the range and the image In the example above, both the possible and actual pets have their own object types, namely Animals and Pets. This model corresponds to the way people normally refer to mappings, as in "People have animals as pets", so requirements gathering is easier. It has more overhead than the other two techniques, because there are two object types instead of one. 2) Just the range If no new features apply to the image, then it is not necessary to model it. For example, if the model says nothing new about pets, it can be omitted. If the pet concept is needed on occasion, then the user can test whether a particular animal has an owner to see if it is a pet. If the pet concept is needed a lot, then this is not the best technique. The minimum cardinality on the ObjectType side of the hasImage/IsImageOf meta-relation is zero so that it is not necessary to model the image. 3) Just the image For example, the Pet-Of mapping may be modelled only between Person and Pet. This technique is best when the context of an application assumes pets, because there is no need to model the mapping to animals. If the requirements are being gathered in a wider context, however, it is best to model that people have animals as pets. Notice we aren't really eliminating the range, since it is needed to determine the legal outputs of the mapping. We are just restricting the range to be identical to the image, or in other words, moving the mapping down from the range to the image.