To tell if a graph represents a function, use the vertical line test :
- Imagine or draw vertical lines at various points along the x-axis on the graph.
- If any vertical line intersects the graph more than once , the graph does not represent a function.
- If every vertical line intersects the graph at most once , the graph does represent a function.
This test works because a function can have only one output (y-value) for each input (x-value). If a vertical line crosses the graph multiple times, it means one x-value corresponds to multiple y-values, which violates the definition of a function
. In summary:
- Passes vertical line test → Graph is a function.
- Fails vertical line test → Graph is not a function.
Additionally, once a graph is confirmed to be a function, the horizontal line test can be used to check if it is one-to-one (each output corresponds to exactly one input)
