Question

which graph does not show a function?

Explanation:

Step1: Recall Vertical Line Test

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

Step2: Analyze Each Graph

• Top - Left: A straight line, vertical line test passes (one intersection per vertical line).
• Top - Right: Check vertical lines. Some vertical lines will intersect multiple horizontal segments (e.g., a vertical line through \(x = - 3\) will intersect two segments), so vertical line test fails.
• Bottom - Left: A parabola opening downward, vertical line test passes (one intersection per vertical line).
• Bottom - Right: A piece - wise linear graph, vertical line test passes (one intersection per vertical line).

Answer:

The graph at the Top - Right (the second graph in the top row)