Question

Which relation is a function?



Responses

a A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.
Image with description A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.

b A coordinate grid containing a U shaped graph with arrows on its ends. The U shape opens upwards and the bottom of the U shape is located at the origin.
Image with description A coordinate grid containing a U shaped graph with arrows on its ends. The U shape opens upwards and the bottom of the U shape is located at the origin.

c A coordinate grid with the graph of a circle centered at the origin and passing through the point begin ordered pair 2 comma 1 end ordered pair.
Image with description A coordinate grid with the graph of a circle centered at the origin and passing through the point begin ordered pair 2 comma 1 end ordered pair.

d Coordinate grid with graph of a vertical line at x equals 3.
Image with description Coordinate grid with graph of a vertical line at x equals 3.

Answer 1

Answer: b.

Reason: Use the vertical-line test. The upward-opening U (option b) passes the test — each x has exactly one y. The right-opening U (a) and the circle (c) fail because some vertical lines hit them twice. The vertical line x = 3 (d) also fails because a single x-value would correspond to infinitely many y-values.