LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

RELATION & 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.**