Vertical Line Test

​Functions

Recall that functions are relations where every "x" value has just one "y" value. This means that the line of every graphed function will have (x, y) coordinates where no "x" is associated with more than one "y". So if we could imagine drawing a vertical line anywhere along a graphed function, our vertical line would not cross the function more than once.

Subject | Subject

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Notice the graphed equation on the left can only be crossed once, making it a function. At the same time the graphed equation on the right could be crossed twice by a vertical line, meaning it cannot be a function.

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​Comparison:

Notice how the one of the imaginary dotted lines crosses the graphed equation more than once?

That means this is not a function.​

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​Example:

Notice how the imaginary dotted line crosses the graphed equation only once?

That means this is a function.​

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​Example: