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.
A function is denoted as y = g (x), where x is the argument or input of the function. We know that x=-1, this means that in order to get g(-1) we should replace x with -1.
