Question

which of these relations are functions? select all that apply.

Explanation:

Step1: Recall the vertical line test

A relation is a function if every vertical line intersects the graph at most once.

Step2: Analyze the first graph

For the first graph, any vertical line will intersect it at most once. So it passes the vertical line test and is a function.

Step3: Analyze the second graph

For the second graph, there exist vertical lines that will intersect it more than once (due to the "S" shape). So it fails the vertical line test and is not a function.

Answer:

The first graph (the one with the curve that does not have a self - intersection in the vertical direction) represents a function.