Question

which of these relations is a function?

Explanation:

Step1: Recall the vertical - line test

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

Step2: Analyze the 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 the second graph

The second graph (a circle) fails the vertical - line test. A vertical line can intersect a circle at two points.

Step4: Analyze the third graph

The third graph (a curve with a vertical asymptote) fails the vertical - line test. A vertical line in the region of the vertical asymptote can intersect the graph multiple times.

Step5: Analyze the fourth graph

The fourth graph (an ellipse) fails the vertical - line test. A vertical line can intersect an ellipse at two points.

Answer:

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