![]() If your vertical line intersects the graph only once, then the relation is a function. Step Three: Based on the number of intersections, determine whether or not the relation is a function. Step Two: Note how many times the vertical line(s) that you drew intersected the graph (either coordinate points or a line/curve). Step One: Observe the given graph and draw one or multiple vertical lines through the graph. The vertical line test is a simple and straightforward tool for determining whether not the graph of a relation represents a function or not.Īpplying the vertical line test is as easy as following these 3 easy steps: The Vertical Line Test Explained in 3 Easy Steps We already know that the graph in Figure 05 represents a function and that the graph in Figure 06 does not represent a function because we already applied the definition of a function to the corresponding mappings.īut what if we had to make this determination using only the graph without the mappings? This is where the vertical line test comes into play. Let's revisit the relations shown in Figure 03 and Figure 04, but this time we will represent them graphically: Now, let's find out how the vertical line test works with realistic examples.Īgain, for a relation to be a function, the relation must have exactly one output for a given input. The Vertical Line Test helps you to determine if a given relation is a function. Now that you understand how to determine whether or not a relation is a function by looking at a mapping, you are ready to learn to make this same determination just by looking at a relation’s graph and using a tool called the vertical line test. In other words, a relation represents the relationship between an input and an output, while a function-more specifically-is a type of relation where there is only one output for each input. Simply put, all functions are relations, but not all relations are functions. What is the difference between a relation and a function?įunctions are a subset of relations. The figures below show a graphic and map representation of the relation between a set of numbers and the square of those numbers. Mappings and graphs are the most common ways of representing relations. This free Vertical Line Test step-by-step guide will teach you how to figure out whether or not a relation is or is not a function by looking at its graph and using a simple mathematical tool called the vertical line test.īefore you learn how to use the vertical line test, we will do a quick review of some very important vocabulary and definitions related to functions and relations.Īre you ready to get started? Vertical Line Test Definitions and Vocabularyĭefinition: A relation is how a set of inputs and outputs of a system are related to each other. ![]() Luckily, there is a simple and handy tool called the vertical line test that you can always use to see if a relation can be considered a function or not just by looking at its graph. Learning how to identify whether or not a given relation is a function is an extremely important math skill (most notably in pre-algebra and algebra). What is the Vertical Line Test in Math? Key Question: What is the vertical line test function and how can it be used? ![]()
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