An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 6 to 6 in increments of 1. A semicircle is graphed on the plane. The semicircle passes through points plotted at coordinates left parenthesis 0 comma 6 right parenthesis, left parenthesis 6 comma 0 right parenthesis, and left parenthesis 0 comma negative 6 right parenthesis.

Question

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

(1 point)
Responses

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

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

The relation is a half-circle.
The relation is a half-circle.

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

Answer 1

To determine if the given relation is a function using the vertical line test, we need to check if any vertical line drawn on the graph intersects the relation at more than one point.

Since the described relation is a semicircle, it would look like a half-circle (either the upper half or the lower half). For a semicircle, when we draw a vertical line, it will intersect the semicircle at most once (if it intersects at all), since there is no section of the graph where it dips back down.

In this case, because the graph of a semicircle only intersects any vertical line once (for the upper half) or does not intersect at all (for the lower half), we conclude that:

Yes, the given relation is a function.