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 (top - left) has a point where a vertical line would intersect it more than once (the two blue lines meet at a point, and a vertical line through that x - value would intersect multiple times), so it's not a function.

Step3: Analyze the second graph

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

Step4: Analyze the third graph

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

Step5: Analyze the fourth graph

The fourth graph (bottom - right, a circle) also fails the vertical line test. A vertical line through the center (along the y - axis) will intersect the circle at two points, so it's not a function.

Answer:

The graph on the top - right (the second graph)