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If a vertical line intersects the graph in some places more than once, then the relation is NOT a function. Here are some examples of relations that are also functions because they pass the vertical line test.
Nov 11, 2022 · If your vertical line intersects the graph more than once at any point, the relation is not a function. We can apply the vertical line test to the graphs from Figure 05 and Figure 06 below to confirm what we already knew (that one graph represents a function and the other does not).
states that if a vertical line intersects the graph of the relation more than once, then the relation is a NOT a function. If you think about it, the vertical line test is simply a restatement of the definition of a function .
The Rule. If every vertical line intersects with a graph at only one point, the graph represents a function. If you can find a vertical line intersecting the graph at more than one point, it doesn’t represent a function.
If any vertical line intersects a graph more than once, the relation represented by the graph is not a function. Notice that any vertical line would pass through only one point of the two graphs shown in parts (a) and (b) of Figure 13.
Thus if a vertical line intersects the graph at more than a point, then it is interpreted as a function having more than one output, which shows it cannot be a function.
If any vertical line intersects the graph more than once, then the graph does not represent a function. Figure \(\PageIndex{12}\) The vertical line represents a value in the domain, and the number of intersections with the graph represent the number of values to which it corresponds.
