Question

which graph represents a function?

Explanation:

Step1: Recall the vertical line test

A graph represents a function if no vertical line intersects the graph at more than one point. In terms of discrete points (like in these graphs), this means each \( x \)-value (horizontal coordinate) should correspond to only one \( y \)-value (vertical coordinate).

Step2: Analyze each graph

• First graph: Check \( x \)-values. Some \( x \)-values have multiple points (e.g., look for repeated \( x \)-coordinates with different \( y \)-coordinates). So it fails the vertical line test.
• Second graph: Each \( x \)-value (the horizontal position of each dot) has only one \( y \)-value. No two dots share the same \( x \)-coordinate. So it passes the vertical line test.
• Third graph: Some \( x \)-values have multiple dots (same \( x \), different \( y \)), so it fails.
• Fourth graph: One \( x \)-value (the vertical line at that \( x \)) has multiple \( y \)-values (the dots stacked vertically), so it fails.

Answer:

The second graph (from the left) represents a function.