Vertical Line Test: Definition & Examples

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  • 0:02 The Function Machine
  • 0:45 Mathematical Functions
  • 1:45 The Vertical Line Test
  • 2:37 Examples
  • 3:09 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

The vertical line test is a quick way to determine if a given relationship is a function. In this lesson, you'll learn more about functions and how the vertical line test can be used to recognize a function.

The Function Machine

In mathematics, a function is a relationship between a set of inputs and their corresponding outputs. An easier way to think of it is that a function is a machine that when you put something in it, it follows a certain set of rules to create a unique product. An example might be a fictional knitting machine. When a particular color of yarn is added, the machine does its thing and produces a specific item of clothing. Each color that is put in the machine can only produce one product. So, if red yarn added to the machine produces a sweater today, it cannot produce a hat tomorrow. It will always produce a sweater. That is what makes it a function.

Mathematical Functions

With mathematical functions, the concept is the same, but not always as obvious. For every function, there is an input and output. A simple function would be: 2x - 7 = y. So, for every number that you can think of to substitute for x, you will get a unique value for y. Often these are written as a table of values.


There are some mathematical equations that are not functions. This is because there is not one unique output for every input. An example of this type of equation would be x = y^2. If the input (or x value) is 4, then the output (y value) could be 2 or -2.

Unfortunately, it can be difficult to determine if an equation is a function just by looking at it, especially with more complex equations. You could just plug in some numbers to test it, but with this method you would have to test every number to be sure. And nobody wants to spend that much time on one problem.

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