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 the graph at most once.

Step2: Test the first graph (ellipse)

Draw a vertical line (e.g., \(x = 0\)). It intersects the ellipse at two points. So, not a function.

Step3: Test the second graph (arrow - shaped)

Draw a vertical line. It intersects the graph at two points (where the "V" is). So, not a function.

Step4: Test the third graph (S - shaped)

Draw a vertical line. It intersects the graph at two points. So, not a function.

Step5: Test the fourth graph (line)

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

Answer:

The graph at the bottom right (the line)