Use the image to answer the question.

Question

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.

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.

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.

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

Yes, the given relation is a function.

Answer 1

To determine whether the relation represented by the semicircle is a function, we can apply the vertical line test. The vertical line test states that if any vertical line intersects the graph of a relation at more than one point, then the relation is not a function.

In the case of a semicircle, any vertical line drawn will intersect the semicircle at two points (except at the endpoints of the semicircle). For example, if you draw a vertical line at x = 0 or x = 3, it will intersect the semicircle at two different y-values.

Since vertical lines can intersect the semicircle at more than one point, we conclude that the relation is not a function.

Therefore, the correct response is:

No, the given relation is not a function.