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: Test the first graph

The first graph (top - left) has a curve that a vertical line would intersect more than once (it has a "S" shape), so it's not a function.

Step3: Test the second graph

The second graph (top - right) is a curve. For any vertical line, it will intersect the graph at most once. So it passes the vertical line test.

Step4: Test the third graph

The third graph (bottom - left) is a circle. A vertical line through the circle will intersect it at two points, so it's not a function.

Step5: Test the fourth graph

The fourth graph (bottom - right) is an ellipse. A vertical line through the ellipse will intersect it at two points, so it's not a function.

Answer:

The graph on the top - right