Question

which of these relations is a function?

Explanation:

To determine which relation is a function, we use the vertical line test: a graph represents a function if no vertical line intersects the graph more than once.

Step 1: Analyze the first graph (top - left)

This graph has a curve that loops, so a vertical line would intersect it more than once. Thus, it is not a function.

Step 2: Analyze the second graph (top - right)

This graph has two separate parts where a vertical line could intersect two points at the same x - value (the "V" part and the other segment). So, it fails the vertical line test and is not a function.

Step 3: Analyze the third graph (bottom - left)

This graph has a curve that loops, so a vertical line would intersect it more than once. Thus, it is not a function.

Step 4: Analyze the fourth graph (bottom - right)

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

Answer:

The relation represented by the bottom - right graph (the straight - line graph) is a function.