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 (circle)

Draw a vertical line through the circle. It intersects the circle at two points, so it's not a function.

Step3: Test the second graph (wavy line)

Draw any vertical line. It intersects the graph at most once, so it passes the vertical line test.

Step4: Test the third graph (ellipse)

A vertical line through the ellipse intersects at two points, so it's not a function.

Step5: Test the fourth graph (figure - 8 like)

A vertical line through it intersects at two points, so it's not a function.

Answer:

The graph in the top - right (the wavy line graph)