Is the following relation a function? x y 6 -1 -1 2 4 3 0 3

Given relation is a function

A relation is said to be a function if no value in its domain is paired up with more than one value in its range.

Since x values represent the Domain of a relation and y values represent the Range of a relation, in terms of x and y we can say:

A relation is said to be a function if an x-value is not paired up with more than one y-value.

From the above table we can see that all the x values are distinct, so no x value is paired with more than one y-value and thus given relation is a function. 

Note that the input values {6, -1, 4, 0} are unique (all different).  So, yes, this relation is a function.  If the input values were  {6, -1, 4, -1, 0}, then no, that would not represent a function because the input values were not unique.