Question

which of these relations is a function?

Explanation:

Step1: Recall vertical - line test

A relation is a function if any vertical line intersects the graph of the relation at most once.

Step2: Analyze first graph

The first graph (a V - shaped graph) passes the vertical - line test. For any vertical line drawn, it will intersect the graph at most once.

Step3: Analyze second graph

The second graph fails the vertical - line test. There are vertical lines that can be drawn which will intersect the graph more than once.

Step4: Analyze third graph

The third graph (a circle) fails the vertical - line test. There are vertical lines that will intersect the circle at two points.

Step5: Analyze fourth graph

The fourth graph fails the vertical - line test. There are vertical lines that will intersect the graph more than once.

Answer:

The first graph (the V - shaped graph) is a function.