# CLASS-11RELATION & FUNCTION - FUNCTION AS A TYPE OF MAPPING

Function as a Type Of Mapping

A function is also thought of as a mapping of its domain into its range.

Function as a mapping

This mapping is not a function.

For the definition of a function to be satisfied, it is essential that each element of the domain is mapped into a unique element of the co-domain. If this condition is not met, the mapping is not a function. In terms of the pictures, for a mapping to be function, each arrow should emanate from a different point in the domain. Whether they terminate at the same point in the codomain is immaterial in the definition.

Remark consider the following mapping. From the figure displaying the association of a player to the game he or she plays, we observe that the player C.Ronaldo of set A is not associated with any game in set B.

Remark – consider the following mapping. From the figure displaying the association of a player to the game he or she plays, we observe that the player C.Ronaldo of set A is not associated with any game in set B.

This association or mapping is not a function.

This association or mapping is not a function.

Essential Requirements For The Definition Of a Function

A function f : A → B is defined under the following condition –

(i) Every x ∈ A is associated with some y in B, i.e., a function is defined only when the domain is entirely “used up”. The set B may not be entirely “used up” by the function.

(ii) The function may associate more than one ‘x’ to the same ‘y’.

(iii) No element in A should have more than one image in B.