Vertical Line Test Math Example

On a graph the idea of single valued means that no vertical line ever crosses more than one value.

Vertical line test math example. In mathematics the vertical line test is a visual way to determine if a curve is a graph of a function or not. The graphs of functions can be straight lines or segments curves or even just a set of points. The equation of a vertical line always takes the form x k where k is any number and k is also the x intercept. 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. The vertical line test is a visual test that you can use to quickly check and see if a graph represents a function. If you can not then the graph represents a function. Vertical line test strategy try to draw a vertical line on the graph so it intersects the graph in more than one place.

The line has to be vertical as illustrated above. In order to be a function each x value can only be paired with exactly one y value. Next we show you a few examples where the vertical line test was used to determine if the graph is a function. But not all graphs represent functions.

States that if a vertical line intersects the graph of the relation more than once then the relation is a not a function. Some types of functions have stricter rules to find out more you can read injective surjective and bijective. The vertical line test supports the definition of a function. You will see a correct vertical line test and an incorrect vertical line test.

Then take a vertical line like a ruler and pass it over the graph. 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. If it crosses more than once it is still a valid curve but is not a function. My examples have just a few values but functions usually work on.

X 4 4 4. Some examples showing how to use the vertical line test to check if a relation is a function or not. That is every x value of a function must be paired to a single y value. 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.

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. The vertical line test is performed by sketching a graph of the equation or by using a calculator to draw it for you. Vertical lines help determine if a relation is a function in math.