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.

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 relation represented by the semicircle is a function, we can apply the vertical line test. This test states that if any vertical line drawn on the graph intersects the graph at more than one point, then the relation is not a function.

In the case of a semicircle, there will be vertical lines that intersect the semicircle at two points in certain sections (for example, on the left and right halves of the semicircle). This indicates that for some x-values, there are multiple corresponding y-values, which means the relation fails the vertical line test.

Therefore, the correct response is:

No, the given relation is not a function.