How to Use and Draw Mapping Diagrams

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  • 0:03 What Are Mapping Diagrams?
  • 0:55 Using Mapping Diagrams
  • 1:27 Creating a Mapping Diagram
  • 4:05 Mapping Diagrams and Graphs
  • 4:38 Lesson Summary
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Lesson Transcript
Instructor: Michael Quist

Michael has taught college-level mathematics and sociology; high school math, history, science, and speech/drama; and has a doctorate in education.

When you're working with functions, mapping diagrams are a great way to see and track the ways your inputs are related to your outputs. In this lesson, we will learn how to use and draw a mapping diagram.

What Are Mapping Diagrams?

Have you ever watched a waitress as she takes orders for drinks from a large table? How does she keep track of which drink goes with which customer? Of course, sometimes they don't, but sometimes it's amazing how they track every drink at the table without looking at a diagram or anything.

Imagine our poor waitress has 12 people at a large table, and she wants to keep track of all the drink orders. She could use a mapping diagram. A mapping diagram helps you to remember relationships between one set of values and another set, or how they're paired together. For example, let's see if we can give our waitress a little help:

She numbers the customers in a clockwise order, lists the drinks as they show up in the orders, and then draws arrows between the customer numbers and the drink name. She has created a mapping diagram.

Mapping diagram for the waitress
waitress example

Using Mapping Diagrams

Mapping diagrams are useful when we're working with functions. They allow us to track the relationship between the inputs (the numbers you're putting into the 'machine') and the outputs (the numbers that are coming out). We can use the diagram to show which input values are tracked to which output values. They also help us make sure a function really is a function.

For example, say we have the following set of pairs, where the first number is the input and the second number is the output.

Mapping diagram for input and output values
mapping diagram 1

Creating a Mapping Diagram

When we construct a mapping diagram from the list of input and output values, we'll draw an area for the inputs and an area for the outputs. We'll list the inputs and outputs in their own areas and then draw arrows to show which input value leads to which output value.

Notice each number from the inputs is tied to only one of the outputs. In math, that's the test for a function. Remember, a function must assign only one output value for each possible input. If any input value has more than one output, then you may have a relationship, but it's not technically a function. Let's look at one that's like that:

This is not a function!
mapping diagram 2

Can we create a mapping diagram from a function that is an equation? Absolutely! All you have to do is decide what input values you want to work with and then plug them into the equation. Your output values will be whatever you get from the equation.

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