Question

which of these relations is a function?

Explanation:

Step1: Recall Vertical Line Test

A relation is a function if no vertical line intersects its graph more than once.

Step2: Test Top - Left Graph

Draw a vertical line (mentally) on the top - left graph. For any x - value, the vertical line intersects the graph at most once. So it passes the vertical line test.

Step3: Test Top - Right Graph

Draw a vertical line on the top - right graph. For any x - value, the vertical line intersects the graph at most once. So it passes the vertical line test.

Step4: Test Bottom - Left Graph

Draw a vertical line on the bottom - left (circle) graph. There are x - values where a vertical line intersects the circle at two points. So it fails the vertical line test.

Step5: Test Bottom - Right Graph

Draw a vertical line on the bottom - right graph. For any x - value, the vertical line intersects the graph at most once. So it passes the vertical line test.

(Note: If we assume the question is to identify which are functions, the top - left, top - right, and bottom - right graphs are functions. If it's a multiple - choice with these four as options, we can specify the correct ones. But from the visual, the bottom - left (circle) is not a function, others are. )

Answer:

The Top - Left Graph, The Top - Right Graph, and The Bottom - Right Graph (or specify based on the exact question context. If it's a single - choice among the four, and the options are the four graphs: The Bottom - Left Graph is not a function, so the other three are functions. If the question is to pick one, any of the top - left, top - right, or bottom - right graphs. For example, if we consider the top - left as a common function - like (absolute value) graph, we can say "The Top - Left Graph" or more precisely based on the visual. )