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 negative 5 comma 0 right parenthesis, left parenthesis 0 comma 5 right parenthesis, and left parenthesis 5 comma 0 right parenthesis.

The graph of a relation is given. Apply the vertical line test to determine if this relation is a function. Enter 1 if the relation is a function. Enter 2 if the relation is not a function.(1 point)

it isnt 2

Answer 1

To determine if the relation represented by the semicircle is a function, we can use the vertical line test. According to this test, if a vertical line intersects the graph at more than one point, then the relation is not a function.

In the case of a semicircle, a vertical line drawn through the center of the semicircle (specifically between the endpoints of the semicircle) will intersect the graph at two points (one on the upper half of the semicircle and one on the lower half, if extended). This means that there are multiple y-values for some x-values.

Since the relation does not pass the vertical line test, it is not a function.

Therefore, the correct answer is:

2 (the relation is not a function).