Mapping and Function
Assignment Mapping: suppose we can assign each element x of a set X in a way, a unique element y of a set Y written as y=f(x) then this is called an assignment mapping.
Domain: the set S is called a domain of the mapping , while the set Y is called the co-domain of the mapping.
the element x of the set X is called the pre-image while the element y of the set Y is called the image of x.
the subset of the co-domain which is the set of all the elements f(x) is called the Range or Image of f. this range of f or image of f is denoted R. Imf or f(x).
Example: Let f assign to each state of  nigeria its Governor. the domain  f  is the set of states in nigeria, the co-domain of f is the governors of states in nigeria.
Example: Let g assign to each country of west africa its capital. the domain of g is the set of countries in west Africa while the co-doamin in the set of capital cities in west Africa. the image of Nigeria is Abuja while the image of Ghana is Ghana is Accra, i.e  g(Nigeria)=Abuja and g(Ghana)=Accra.
Example: Let  X={p,q,r,s} and Y={p,q,r}. Let f  be a mapping of X into Y defined by f(p)=q,f(q)=r,f(r)=r and f(s)=q. hence the domain is X and the co-domain isY. by this definition the image of p is q.