Lesson 4.4

Domain and Range (Discrete)

Every function has boundaries. The Domain is what you can put in. The Range is what you can get out.

Introduction

A function consists of two sets. The Domain is the set of all possible inputs (x-values). The Range is the set of all possible outputs (y-values). When dealing with a list of points (Discrete), we just list them in curly brackets.

Past Knowledge

Lesson 4.2 (Relations). We are just naming the "Input" and "Output" columns.

Today's Goal

Write the Domain and Range for a set of points using set notation .

Future Success

Recognizing domain helps avoid dividing by zero or taking square roots of negative numbers later.

Key Concepts

Defining the Sets

DOMAIN

All Inputs

Left / Right

Dependent Variable

RANGE

All Outputs

Up / Down

Independent Variable

DIX ROY
Domain, Input, X | Range, Output, Y

Worked Examples

Example 1: Identify from Points

Basic

Find the domain and range of:

Find Domain (X)

Grab the first number of each pair: 2, -1, 0.

Domain:

*Usually best to write in order from least to greatest.

Find Range (Y)

Grab the second number: 5, 3, 5.

Range:

*Notice we only wrote 5 ONCE. No repeats in sets!

Example 2: From a Mapping Diagram

Intermediate

Input

→

Output

Just list them!

Domain =

Range =

Example 3: From a Table with Repeats

Advanced

Find the domain and range from the table below.

	-4	1	3	1	-4
	7	0	-2	7	0

List All X-Values

Read across the top row: -4, 1, 3, 1, -4.

Remove Duplicates & Sort

Cross out repeats: 1, -4. Sort: -4, 1, 3.

Domain:

Repeat for Y-Values

Bottom row: 7, 0, -2, 7, 0. Sort: -2, 0, 7.

Range:

Domain: | Range:

Common Pitfalls

Writing Repeats

If the range is 5, 5, and 8, just write . Sets are like guest lists; you don't list the same person twice.

Identifying the Wrong Variable

Remember "DIX ROY". Domain is Input (X). Students often accidentally swap them.

Real-Life Applications

Menu Pricing: A menu is a function. The Domain is the list of items (Burger, Fries, Soda). The Range is the list of prices ($5, $3, $2). You can't order something not on the menu (Domain Error!).