Question

which of these relations is a function?

Explanation:

Step1: Recall the vertical line test

A relation is a function if every vertical line intersects its graph at most once.

Step2: Analyze the first graph

The first graph has two lines meeting at a point. A vertical line (not at the meeting point) would intersect two lines, so it fails the vertical line test.

Step3: Analyze the second graph

For the second graph (the curve), any vertical line will intersect the curve at most once. So it passes the vertical line test.

Step4: Analyze the third and fourth graphs (ellipses)

Ellipses (third and fourth graphs) are symmetric, and a vertical line will intersect them at two points, so they fail the vertical line test.

Answer:

The relation represented by the second graph (the curve) is a function.