Vertical Line Test Math Example

Some examples showing how to use the vertical line test to check if a relation is a function or not.

Vertical line test math example.

The vertical line test supports the definition of a function. On a graph the idea of single valued means that no vertical line ever crosses more than one value. Some types of functions have stricter rules to find out more you can read injective surjective and bijective. My examples have just a few values but functions usually work on.

The equation of a vertical line always takes the form x k where k is any number and k is also the x intercept. In order to be a function each x value can only be paired with exactly one y value. The graphs of functions can be straight lines or segments curves or even just a set of points. A function can only have one output y for each unique input x if a vertical line intersects a curve on an xy plane more than once then for one value of x the curve has more than one value of y and so the curve does not represent a function.

In mathematics the vertical line test is a visual way to determine if a curve is a graph of a function or 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 it crosses more than once it is still a valid curve but is not a function. The vertical line test can be used to determine whether a graph represents a function.

If you can not then the graph represents a function. The line has to be vertical as illustrated above. You will see a correct vertical line test and an incorrect vertical line test. The vertical line test is a visual test that you can use to quickly check and see if a graph represents a function.

For instance in the graph below the vertical line has the equation x 2 as you can see in the picture below the line goes straight up and down at x 2. Then take a vertical line like a ruler and pass it over the graph. The vertical line test. That is every x value of a function must be paired to a single y value.

If we think of a vertical line as an infinite set of x values then intersecting the graph of a relation at exactly one point by a vertical line implies that a single x value is only paired to a unique value of y. Vertical line test strategy try to draw a vertical line on the graph so it intersects the graph in more than one place. If you think about it the vertical line test is simply a restatement of the definition of a function. Is a way to determine if a relation is a function.

Next we show you a few examples where the vertical line test was used to determine if the graph is a function. If we can draw any vertical line that intersects a graph more than once then the graph does not define a function because a function has only one output value for each input value. X 4 4 4.