In order to be a function, a relation must not have any repeated x-values.
So looking into the points of all of the relations listed, we see that in 'a', there are two points sharing the same value of x: (1,-2) and (1,0).
In 'b', we see that there are no repeated x-values.
In 'c', there are two points that share the same x-value: (0,1) and (0,2).
And in 'd', all of the points share the same x-value, being -2.
Therefore, since 'b' is the only choice with no repeated x-values, choice b is the answer.