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Vertical Line Test

Determine if the Graph is a Function

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Average Temperature in Houston

Average Temperature in Houston

Jennifer Ledwith

You can look at a graph to determine if it is a function. The vertical line test tells us that any given vertical line will pass through a function only once.

Every function passes the vertical line test. Draw a vertical line anywhere on the relation. If the vertical line touches the relation at only one point, then the relation has passed the vertical line test and is a function.

Consider an example, the graph, Average Temperature in Houston. Draw a vertical line anywhere on the graph. How many times does the line touch the graph? If you answered only once, then you’re right. The graph describes a function.

Consider another example, a circle. Draw a circle on a sheet of paper. Draw a vertical line anywhere on the circle. How many times does the line touch the circle? The vertical line passes through the circle at 2 points. Therefore, the circle is not a function.

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