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's not a function.

Step3: Analyze the second graph (S - shaped curve)

A vertical line will intersect this curve at more than one point, so it's not a function.

Step4: Analyze the third graph (polynomial - like curve)

For any vertical line, it will intersect this graph at most once. So it passes the vertical line test.

Step5: Analyze the fourth graph (curved with crossing)

A vertical line will intersect this graph at more than one point, so it's not a function.

Answer:

The graph in the bottom - left (the third graph)