Well, to determine if a relationship was a function, we had to utilize tables and mappings earlier. We can now readily deduce this from a graph – how? The answer is the Vertical Line Test. The main usability of the test lies in the fact that it helps to determine if a graph is a function.
But what is the vertical line test basically? What are some examples of it? To get the answer to these questions, stay tuned with us and read this guide till the end.
What Is Vertical Line Test Definition?
The vertical line test in mathematics is basically a visual approach. It helps in assessing whether or not a curve is basically a graph of the function. For each unique input, X, a particular function must have a single output, Y. If a vertical line crosses a curve on an XY plane many times, the curve has more than one value of y for one value of X. Hence, it does not represent a function. When all vertical lines cross a curve just once, the curve is said to have a function.
What Is Vertical Line Test Function?
Before jumping on to the vertical line test function, let’s give you an idea of what is ‘Function’ in mathematics. In mathematics, a function is a rule, an expression, or a law that describes the connection between a variable (the independent variable) and then another variable (the dependent variable).
To establish if a graph reflects a function, you can apply the vertical line test. Because a function only has a single output value for every input value, if we can sketch a vertical line crossing a graph more than once, the graph does not constitute a function. Graphs are usually drawn with the input values on the horizontal plane and the output values on the vertical axis, as is customary. A curve is considered to have a function when all vertical lines intersect it only once.
Below are the two images that explain the vertical line test function. Take a look:
NOT A FUNCTION & FUNCTION
How To Use Vertical Line Test In A Graph To Denote The Graph Represents A Function?
So, here is a takeaway from what you have learned above. How to implement the vertical line test in a graph for denoting the graph represents a function? Read the bullet points below:
The First Step – Examine the graph to check if any of the sketched vertical lines overlap the curve more than once.
The Second Step – If there is a line like this, the graph isn’t representing a function.
What Are Some Vertical Line Test Examples?
Now that you know what vertical line test definition and vertical line test function are, I hope a suitable example will give you better clarity. Here we have selected a simple one from many complicated vertical line test examples for you:
1. Identification Of Whether A Given Equation Is A Function
With an equation Y square = -5x, graph the line and show that it is a function
The solution: We may deduce that the function’s graph is a parabola expanding to the left by looking at the equation. Let us now solve for the values of y-values for certain x-values to be sure. Substitute x = 0, x = -5, x = -10, x = -25, and x = -40 for x = 0, x = -5, x = -10, x = -10, x = -25, and x = -40.
Then, using the acquired x and y values, construct a vertical line across the graph’s drawing. The vertical line, as you can see in the image below, goes through two spots. As a result of the failure of the vertical line test, the line equation doesn’t indicate a function.
Frequently Asked Questions (FAQ)
Q1. What Is the Vertical Line Test?
Vertical lines meet the graph at least once if no two separate points in the graph have the same initial coordinate. The vertical line test is what it’s called. Graphs of functions are those that satisfy the vertical line test.
Q2. Why Function Is Vertical Line Test?
A graph may be used to represent a function. In a short amount of space, graphs exhibit a large number of input-output pairs. They typically make relationships easier to understand because of the visual information they convey. The vertical line test is highly applicable in order to decide if a graph represents a function.
Q3. What Is The Horizontal Line Test?
Horizontal lines intersect the graph at least once if no two separate points in the graph have the same second coordinate. That is known as the horizontal line test is. One-to-on functions are those whose graphs satisfy the horizontal line test.
Summing It Up
That’s all about the Vertical Line test in mathematics. You will find the maximum application of the vertical line test and vertical line test function in advanced Algebra. I hope the explanation was clear to you and you enjoyed reading the article. Do let us know your opinions if you have any in the comment section below. Also, do not hesitate to let us know if you get any questions regarding this.