A vertical line test is a visual way to determine if the graph of a relation is a function.
If the vertical line passes through at least two points on the graph, then 1 element in the domain is paired with more than 1 element in the range.
The line has to be vertical. Below see a correct vertical line test and an incorrect vertical line test.
Next, we show you a few examples where the vertical line test was used to determine if the graph is a function.
Example #1
Notice the two blue points. This means that the vertical line passes through 2 points.
Can you guess what these two points are just by looking at the graph?
These two points are (4, 1) and (4, 3). As you can see, 4 is paired with two elements and again that is why it is not a function.
Example #2
Here, there are 5 vertical lines and none of them passes through at least 2 points. Therefore, this graph is a function.
Feel free to draw as many vertical lines as possible before you draw your conclusion.
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