1.1 Functions

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Objectives:

• Determine when a relationship is a function and determine its inputs and outputs
• Represent relations/functions as tables, ordered pairs, graphs, equations, etc.
• Review graphs and the vertical line test

Definitions

function

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Lesson Guide

Determine when a relationship is a function and determine its inputs and outputs

[15 minutes] Begin this lesson by giving examples of relationships between two sets. Examples should be easy to understand. I.e., use real world examples such as the days of the year and their average daily temperatures or the students in your class and the month they were born. Discuss how we can identify objects in the two sets and call this identification a “relation.”

A lot of this class will be about exploring the relationship between different pieces of  information. For example:

Instructor Example

Suggested Example

This is a sentence that is in place to generate space in the table

The year you were born is related to your age. The month is related to the temperature outside. The price of gold is related to the supply and the demand. If we have a very special kind of relationship called a ``function," we can use one piece of information, called the input, to completely predict the other piece of information, called the output. It is often useful to take a few minutes and draw bubble diagrams of the examples you are going over. E.g.