Answer

{(3, 2), (6, 4), (9, 6), (12, 8)}   is a function

{(2, 3), (2, 5), (3, 6), (9, 4)}    is not a function

{(2, 4), (6, 3), (4, 8), (6, 6)}    is not a function

{(3, 4), (5, 2), (6, 8), (6, 4)}    is not a function

Explanation

To test if a relation is a function from a set of ordered pairs, you just need to check if each element of the domain is paired with exactly one element of the range. Remember that the domain is all the x-values (first points of each ordered pairs) and the range is all the y-values (second points of each ordered pairs).

Let’s test each one of our relations:

{(3, 2), (6, 4), (9, 6), (12, 8)} each element of the domain is paired with exactly one element of the range, so this one is a function.

{(2, 3), (2, 5), (3, 6), (9, 4)}  2 in the domain is paired with both 3 and 5 in the range, so this one is not a function.

{(2, 4), (6, 3), (4, 8), (6, 6)}  6 is paired with both 3 and 6, so this one is not a function either.

{(3, 4), (5, 2), (6, 8), (6, 4)}  6 is paired with both 8 and 4, so this one is not a function either.