Why does the vertical line test tell us whether the graph of a relation represents a function? When a vertical line intersects the graph of a relation more than once, it indicates that for that output there is more than one input, which means the relation is not a function. When a vertical line intersects the graph of a function more than once, it indicates that for that output there is more than one input, which means the function is not a relation. When a vertical line intersects the graph of a relation more than once, it indicates that for that input there is more than one output, which means the relation is not a function.

1. **Definition of a Function:** A function assigns exactly one output for each input. In mathematical notation, for a function \( f \), for every \( x \) in the domain, there is exactly one \( y \) such that \( f(x) = y \). 2. **Vertical Line Test Explanation:** A vertical line represents a constant \( x \) value. When a vertical line intersects a graph, it collects all the \( y \) values corresponding to that particular \( x \). - If the line intersects the graph more than once, it means that there is an \( x \) with more than one corresponding \( y \)-value. - This violates the definition of a function since a function must assign only one \( y \)-value for each \( x \). 3. **Correct Choice:** The correct explanation is: *"When a vertical line intersects the graph of a relation more than once, it indicates that for that input there is more than one output, which means the relation is not a function."* Thus, the right option is the third one.