To determine if a graph is a function, use the vertical line test. This test states that if any vertical line drawn on the graph intersects the graph at more than one point, then the graph does not represent a function. This is because a function can only have one output (y-value) for each input (x-value). If every vertical line intersects the graph at exactly one point, then the graph is a function.
How to perform the Vertical Line Test:
- Imagine or draw vertical lines (lines parallel to the y-axis) across different points of the graph.
- Check how many points the vertical line touches on the graph.
- If any vertical line touches the graph more than once, the graph is not a function.
- If all vertical lines touch the graph only once, the graph represents a function.
This test helps visually confirm the definition of a function, which requires each input to have exactly one output.
