To determine whether a relation is a function, each input (or x-value) in the relation must be associated with exactly one output (or y-value).
Let's examine the relation you provided:
\[ {(0,-1), (3,6),(6,8),(9,12),(0,-1)} \]
In this relation, the x-values are:
- 0 (which appears twice, with the same y-value of -1)
- 3
- 6
- 9
All x-values are unique with the exception of the 0, which still maps to the same y-value (-1). Since each x-value is associated with exactly one y-value, this relation meets the criteria for being a function.
Therefore, this relation does represent a function.
Answer: This relation represents a function.