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Question

Functions Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the 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

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.

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

The relation is a half-circle.

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 a vertical line intersects the graph at more than one point, then the relation is not a function.

In this case, since the relation is a semicircle, you can draw a vertical line that intersects the semicircle at two points at least in its range. Thus, this indicates that there are multiple y-values for some x-values.

Therefore, the correct response is:

No, the given relation is not a function.