A relation is a function if each input (x-value) is associated with only one output (y-value).
Let's check each relation:
1. { (1,0), (2,2), (1,3) }
In this relation, the input 1 is associated with both 0 and 3. It violates the definition of a function.
2. { (1, 2), (1, 4), (2, 6) }
In this relation, the input 1 is associated with both 2 and 4. It also violates the definition of a function.
3. { (2, 1), (2, 2), (2, 3) }
In this relation, the input 2 is associated with three different outputs: 1, 2, and 3. It is not a function.
4. { (0, 0), (4, 0), (6, 0) }
In this relation, each input (0, 4, and 6) is associated with only one output (0). It satisfies the definition of a function.
So, the only relation that is also a function is:
{ (0, 0), (4, 0), (6, 0) }