Question

Which relation is a function?

Responses

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 alt text: 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.

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 alt text: 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.

Coordinate grid with graph of a vertical line at x equals 3.
Image with alt text: Coordinate grid with graph of a vertical line at x equals 3.

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.

Answer 1

The relation that is a function is:

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.

How to identify a function relation?

A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

Looking at the given options, the U-shaped graph that opens upwards and the bottom of the U shape is located at the origin is not a function because it fails the vertical line test.

The circle centered at the origin and passing through the point (2,1) is not a function because it fails the horizontal line test.

The vertical line at x=3 is not a function because it fails the vertical line test.

The U-shaped graph with arrows on both ends that opens to the right and passes through the origin is a function because it passes both the vertical line test and the horizontal line test