What Is Vertical Line Test In Algebra? Is It For Identifying Functions?

The vertical line test is basically used to find out if the given equation in a graph can make a representation of a function or not. There are many to like to know about this test in algebra and here in this article, we are going to talk about this so keep reading.

This test basically states that the vertical line can cut the graph of a particular function only at one single point, then and only then it would be considered as a function. If the vertical line cuts the graph more than one time then that graph can’t be considered as a function. To know more about this line continue reading.

What Is The Vertical Line Test?

Before starting the discussion about the vertical line, we need to know what is it. This line test is basically used in order to ensure that a graph is functional or not. The vertical line represents a set of countless points with the same x coordinate and with different y coordinates for every point. This line has the place in the parallel to the axis of y.

If the vertical line crosses the curve at a specific point then the value of y is one like the x’s value and this is called the function. This test is very helpful if someone wants to know if the relation can be considered as a function or not. The definition of vertical line test actually satisfies the definition of a function in a graph.

In the graph, for every x value, there is a y value that exists in the function. The equation is like this: If the vertical line is x and that is equal to a and x cuts the curve of y then that is equal to y=f which is x but only in one point. Then that curve is y=f which is x and that is considered to be a function. The line should cross the curve in more than one or two specific points for the curve to become a function.

now if the vertical line is x=a and it crosses the graph y=f(x) at only one point then the created two points are (x, y1), (x, y2), then this contains different values of y but it has the same value for x. Here every domain has more than one or two codomain values and this does not fit into the definition of a function and that means that it can not be considered as a function.

In a graph, if the domain has two or more than one value then it can not be considered as a function. In a function, there can be only one output for every input. This is the answer to the question that asks what is the vertical line test.

Explain What The Vertical Line Test Is And How It Is Used?

In order to apply the vertical line test and get to know if the graph is a function or not you have to follow some needed steps. There are basically two methods that can be applied in order to do the vertical test. The two methods are geometrically and algebraically. Now let’s discuss about that.

Geometrically

Here you have to draw the graph of y that is equal to f(x). Now you have to draw the line x=a and you have to also focus on the number that cuts the curve in the graph which means its y=f(x). If this line crosses the curve two times or just more than one time then that is not considered to be a function. But if the vertical line crosses the curve at just one time then it is a function.

Algebraically

Here the equation is like that: the vertical line is equal to x=a and the curve equation is y=f(x). So here we get y=f(a). If in the curve you get more than one value of y then the equation is going to be y=f(x) and that is not considered to be a function.

Here is the answer to the question that asks to explain what the vertical line test is and how it is used.

Vertical Line Test Function

Sometimes the vertical-line test is used to determine the representation of a graph in a function. If anyone draws more than one vertical line in a graph then the graph can not be considered as a function anymore.

A graph that represents the function has only one output for only one input value and this is the answer to your question that asks what is vertical line test function is.

Vertical Line Test Examples

We talked a lot about this topic and now we are going to provide you with some vertical line test examples so that you can understand the concept completely. Here are the examples:

Conclusion

This article starts with a question that asks what is vertical line test in Algebra and what are the identifying functions of this line test and we tried our best to give you a proper answer to your question.

Hope you are satisfied with the answer we have provided you. To wrap it up we can say that the vertical test is a very useful test in Algebra and it is good that you want to gather knowledge about this topic.

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