2.2: Domain and Range

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Page ID: 203383

Roy Simpson, Cosumnes River College
Cosumnes River College

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Prerequisite Skills

Sets and Numbers
- Inequalities and Inequality Notation
- Intervals and Interval Notation
Factoring Techniques
- Factoring Difference of Squares
Solving Inequalities
- Solving Linear Inequalities
- Solving Compound Inequalities
- Solving Quadratic Inequalities (sign chart method)
Graphs
- Closed- and Open-Circle Notations

Finding the Domain of a Function Defined by an Equation

MyOpenMath $ \PageIndex{ 3 } $: Finding the domain and range of a relation given as a set of ordered pairs

MyOpenMath $ \PageIndex{ 9 } $: Finding the domain of a quadratic function

MyOpenMath $ \PageIndex{ 11 } $: Finding the domain of a rational function

MyOpenMath $ \PageIndex{ 15 } $: Finding the domain of a function with an even root

Using Notations to Specify Domain and Range

Definition: Set-Builder Notation

Example: Using different notations

State the solution to the last example using interval, inequality, and set-builder notations.

Finding Domain and Range from Graphs

MyOpenMath $ \PageIndex{ 6 } $: Finding domain and range from a graph

Finding Domains and Ranges of the Toolkit Functions

Let's state the domains and ranges of the Toolkit functions.

Graphing Piecewise-Defined Functions

Definition: Piecewise Function

MyOpenMath $\PageIndex{16}$: Evaluating piecewise functions

Example: Writing a piecewise function

A museum charges $5 per person for a guided tour with a group of 1 to 9 people or a fixed $50 fee for a group of 10 or more people. Write a function relating the number of people, $ n $, to the cost, $ C $.

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MyOpenMath \( \PageIndex{ 3 } \): Finding the domain and range of a relation given as a set of ordered pairs

MyOpenMath \( \PageIndex{ 9 } \): Finding the domain of a quadratic function

MyOpenMath \( \PageIndex{ 11 } \): Finding the domain of a rational function

MyOpenMath \( \PageIndex{ 15 } \): Finding the domain of a function with an even root

Definition: Set-Builder Notation

Example: Using different notations

MyOpenMath \( \PageIndex{ 6 } \): Finding domain and range from a graph

Definition: Piecewise Function

MyOpenMath \(\PageIndex{16}\): Evaluating piecewise functions

Example: Writing a piecewise function

MyOpenMath \( \PageIndex{ 18 } \): Graphing a piecewise function

Definition: Absolute Value Function