To determine if a relation is a function using the vertical line test, you need to check if any vertical line intersects the graph of the relation at more than one point. A relation is a function if each input (x-value) has exactly one output (y-value).
In the case of a half-circle, a vertical line would intersect the half-circle at most one point, indicating that for each x-value, there is only one y-value associated with it.
Therefore, if the relation is a half-circle, the correct response is:
Yes, the given relation is a function.