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 each graph

• First graph: A vertical line would intersect it more than once (has a "S" shape), so not a function.
• Second graph: A vertical line would intersect it more than once (has a "loop" horizontally), so not a function.
• Third graph: Any vertical line will intersect it at most once (passes vertical line test), so it is a function.
• Fourth graph: A vertical line (e.g., through the y - axis intersection) will intersect it more than once (it's a circle), so not a function.

Answer:

The third graph (the one with the wavy curve that passes the vertical line test) is a function.