We are the teachers. We will have to take the initiative to develop the concept of the students. But unfortunately we don’t do that. For example, Calculus is completely a new branch of Mathematics. Before starting calculus the students should have the clear idea about ‘Mapping’ or ‘function’. But most of the students start Calculus from ‘Limit’. And we, the teachers don’t insist them to make the concept in ‘Mapping’. Some students read this chapter but do not form the concept on it.
We can describe the function with the shooting game. In various fare we shoot balloons with air gun.Now think that the packet of the bullet is the domain set and the balloon board is the co domain set. The air gun makes the correspondence between the two sets by obeying some rules.This rule is called mapping.

If one bullet can hit a no.s of balloons, it is an 'ONE TO MANY' mapping.

If more than one bullet is used to hit a of balloon, it is an 'MANY TO ONE' mapping.

If one bullet and one balloon correspondence, it is an 'ONE TO ONE' mapping.

Always remember that the bullets should be exhausted, otherwise the mapping will not be defined. But the some of the balloons may not be hit by the bullets.

If all the balloons are hit by the bullets, it is an 'ONTO' mapping, otherwise it is called an 'INTO' mapping.

The set of burst balloons is called ' RANGE' set.