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 (circle)

A vertical line through the circle will intersect it at two points (except at the top, bottom, left, rightmost points). So it fails the vertical line test.

Step3: Analyze the second graph (S - shaped curve)

A vertical line will intersect this curve at more than one point. So it fails the vertical line test.

Step4: Analyze the third graph (circle on left)

A vertical line through this circle will intersect it at two points. So it fails the vertical line test.

Step5: Analyze the fourth graph (wavy curve)

Any vertical line drawn will intersect this graph at most once. So it passes the vertical line test.

Answer:

The bottom - right graph (the graph with the wavy curve that passes the vertical line test)