Final answer:
The relation {(2,2), (3,3), (4,4), (5,5)} is a function as each input value has one unique output value, whereas {(2,1), (2,3), (-2,5), (-2,7)} is not a function since an input value is paired with multiple outputs.
Step-by-step explanation:
To determine which relation is a function, we need to check if for each input value (x-coordinate) there is exactly one output value (y-coordinate). A function has the characteristic that each input value corresponds to one and only one output value.
The first set of ordered pairs {(2,2), (3,3), (4,4), (5,5)} is a function because each x-coordinate is paired with exactly one y-coordinate.
However, the second set of ordered pairs {(2,1), (2,3), (-2,5), (-2,7)} is not a function because the input value 2 is associated with two different output values (1 and 3), which violates the definition of a function.
Therefore, the relation that is a function is the first one: {(2,2), (3,3), (4,4), (5,5)}.