How To Determine If A Relation Is A Function [Examples Included]

Key Concepts On How To Determine If A Relation Is A Function: 

It is important for students to understand what makes a relation a function before they jump into using the vertical line test. Start by giving students a real scenario that allows them to see that in a function, we cannot have two different outputs when giving the same input. This will allow students to understand what truly makes a relation a function and will give more context to why we can use the vertical line test once it’s introduced.

How do you teach how to determine if a relation is a function?

Introduction

Start by asking students the following question: Can one person be 4 feet and 5 feet tall on their 16th birthday? Allow students to talk or offer possible explanations. Keep in mind that students will figure out ways this may be possible! Allow for a fun conversation but ultimately, make sure it is agreed upon that one person cannot be two different heights at the same time. You can draw this graph on the board and talk through plotting the two points (16, 4) and (16, 5). 

Draw students attention to the fact that these points are in a straight vertical line, since they have the same x-value. Explain that since this one x-value is associated with two different y-values, this cannot be a function!

Determining a function from coordinate points

When looking at a set or ordered pairs, a table of values or a mapping diagram, you can have students ask themselves a few questions to determine if the relation is a function. Remind students that a relation is only a function if each x-value corresponds with only one y-value. The flowchart below can help them organize their thoughts.

Determining a function from a graph: The Vertical Line Test

Now you can more formally introduce the vertical line test. Show students a few examples of graphs and draw vertical lines down them. 

• If ANY of the vertical lines touch the relation more than once, then the relation is not a function. 

• If you can draw a vertical line anywhere on the graph and it will never hit the relation more than once, then the relation is a function. 

Examples

Vocabulary for teaching how to determine if a relation is a function

Relation: A relationship between two sets of values. A relation is often expressed as x-values and y-values of ordered pairs.

Function: A relationship between a set of input values and output values. Each input value (x) will have only 1 output (y) value. 

A rule exists that relates the two sets of data. 

The vertical line test can be used to identify a function on a coordinate plane. 

Also read: How To Convert Standard Form To Scientific Notation

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Misconceptions and errors students are likely to have

• Students might think when a y-value is repeated the relation is not a function.
  • Remind students that repeated y-values are okay. We want to check if there are any repeated x-values. Then see if those corresponding y-values are different. If they are, the relation is not a function.

Resources:

• Downloadable worksheet for practicing determining if a relation is a function
• Quiz for assessing and determining if a relation is a function

Frequently Asked Questions: