Explain why the vertical line test is used to determine if a graph represent a function

Vertical line test tells us whether the graph represents a function or not. This test states that "if a vertical line intersects the graph at only one point then it is a function otherwise not"

Now, if any vertical line intersects the graph at two points then it means that for a value of x, we have to y values. In other words the x value has not unique y values which doesn't satisfy the condition of a relation to be a function.

Therefore, if the vertical line intersects the graph at only point then only each x values has a unique y values.

Please see the attached images. Image 1 is not a function since the vertical line intersects at two points whereas, image 2 represents a function.

Hence, we can conclude that vertical line test is used to determine if a graph represent a function.

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