Question

which of these relations is a function?

Explanation:

A relation is a function if every input (x-value) has exactly one output (y-value). We use the vertical line test: a vertical line drawn anywhere on the graph will intersect the graph at most once.

1. Top-left graph: Fails the vertical line test (some x-values have 2 y-values).
2. Top-right (circle): Fails the vertical line test (most x-values have 2 y-values).
3. Bottom-left graph: Passes the vertical line test (each x has only one y).
4. Bottom-right graph: Fails the vertical line test (one x-value has 2 y-values).

Answer:

The bottom-left graph (the curved relation opening to the left) represents a function.