Identify a function

This lesson will show you how to identify a function using mapping diagrams. What is a function? A function is a relation in which each element of the domain is paired with exactly one element in the range.  

A relation


Looking at the mapping diagram above, the elements in the domain are { -5, 1, 6, 0 } and the elements in the range are { 9, -2, -6, 10 } 

Since 1 is paired with two elements in the range ( 9 and -6 ), the relation is not a function.

A function


For the relation above, notice that each element in the domain is paired with exactly 1 element in the range.

Therefore, this relation is a function. 

A function


Now, what about the last one above? We see that all the elements in the domain are paired with the same element in the range.

What is it also a function? It is still a function because each element in the domain is paired with only 1 element in the range.

For a relation to be a function, it is not necessary that each element in the domain be paired with a different element in the range.

As long as two arrows do not emerge or move out from just 1 element in the domain, we are fine!

How to identify a function with the vertical line test