The graph of a relation is given. Apply the vertical line test to determine if this relation is a function.

Question

(1 point)
Responses

Yes, the given relation is a function.
Yes, the given relation is a function.

There is not enough information to determine whether this relation is a function.
There is not enough information to determine whether this relation is a function.

No, the given relation is not a function.
No, the given relation is not a function.

The relation is a half-circle.

Answer 1

The relation is a function.

Explanation:
The vertical line test states that if there is no vertical line that intersects the graph of a relation more than once, then the relation is a function. In other words, for every x-coordinate, there should only be one y-coordinate.

In the case of a half-circle, for each x-coordinate, there is only one y-coordinate. Therefore, any vertical line will intersect the graph of the relation at most once. This means that the relation satisfies the vertical line test and is a function.