Final answer:
The relation with pairs (0,0), (3,0), and (5,0) is a function because each input has exactly one output associated with it.
Step-by-step explanation:
To determine if a relation is a function, we assess whether each input (x-value) is uniquely associated with one output (y-value). In the given relation with pairs (0,0), (3,0), and (5,0), each distinct input value (0, 3, and 5) corresponds to only one output value (0). This adherence to the one-to-one mapping criterion establishes the relation as a function. The absence of duplicate x-values with differing y-values ensures that each element in the domain (set of x-values) maps uniquely to an element in the range (set of y-values).
In this case, the relation satisfies the fundamental characteristic of a function, providing clarity on the input-output relationships and affirming its functional nature within the context of mathematical analysis.