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 (ellipse)

Draw a vertical line through the ellipse. It will intersect the ellipse at two points. So, it is not a function.

Step3: Analyze the second graph (line)

Draw any vertical line. It will intersect the line at most once. So, it passes the vertical line test.

Step4: Analyze the third graph (curved line)

Draw a vertical line; it will intersect the graph at two points. Not a function.

Step5: Analyze the fourth graph (S - shaped curve)

Draw a vertical line; it will intersect the graph at more than one point. Not a function.

Answer:

The graph in the top - right (the line) is a function.