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 top - left graph

Draw a vertical line (mentally) on the top - left graph. We can see that a vertical line will intersect the graph more than once (because of the "zig - zag" shape), so it is not a function.

Step3: Test the top - right graph

Draw a vertical line on the top - right graph. For any vertical line \(x = a\) (where \(a\) is a real number), the vertical line will intersect the graph at most once. So it passes the vertical line test.

Step4: Test the bottom - left graph

Draw a vertical line on the bottom - left graph. A vertical line will intersect the graph more than once (because of the "corner" and the two - part shape), so it is not a function.

Step5: Test the bottom - right graph (circle)

For a circle centered at the origin (or any circle), a vertical line (e.g., \(x = 0\) for a circle centered at the origin) will intersect the circle at two points (\((0,r)\) and \((0, - r)\) where \(r\) is the radius), so it does not pass the vertical line test.

Answer:

The graph on the top - right