Back To Course

ACT Prep: Help and Review44 chapters | 435 lessons | 26 flashcard sets

Instructor:
*Jennifer Beddoe*

The domain is the group of numbers that can be entered into a function to create a valid output. This lesson will further describe the domain and methods for determining the domain. A quiz at the end of a lesson will test your knowledge.

A **function** describes the relationship between an input and an output. It can be compared to a machine that spits out different items depending on what was put into the machine. Let's take, for example, a fictional shoe machine. The operator puts in a colored disc, and, depending on the color of that disc, a certain shoe is created. So, if a white disc is placed in the machine, it creates a tennis shoe; a black disc creates a loafer; a yellow disc creates a sandal. It's the same each time; never does the machine create a tennis shoe from a yellow disc.

In mathematics, functions are written as equations. They can also be shown as a graph.

A function's input is called the **domain**, and a function's output is called the **range**. The domain relates to the colored discs from the example above, and the range would be the shoes that are created.

The domain of a function is the set of all possible values that *x* can be equal to that will make a valid equation. There are only two instances in which an equation will not be valid - if there is a zero in the denominator or a negative square root. In all other instances, the equation works. Take, for example, the function f(*x*) = *x*^2.

No matter what value we substitute for *x*, the equation will be valid. Therefore, we would say that the domain of this function is all real numbers.

There are two methods used to determine the domain of a function: algebra and graphing.

Look at the following function:

To find the domain of this function, we need to remember the definition of a domain and then do some simple algebra.

One thing we remember about the domain of a function is that it cannot include a negative square root. In order to find the domain, we have to know what numbers make the (*x* + 9) negative and exclude them. To do that, solve the equation:

*x* + 9 ≥ 0

*x* ≥ -9

The domain of this function is *x* ≥ -9.

When you graph a function, the *x*-values signify the domain of that function. You can often determine the domain by looking at a graph.

You can see from this graph that the domain of the function is all real numbers.

Here is another example:

The domain of a function can be written out in words, but to be more mathematically correct, it should be written as an **inequality** or by using **interval notation**. Back to our example:

The domain written as an inequality would be:

*x* ≥ -9, since *x* is equal to all numbers greater than or equal to -9.

Using interval notation, you would write:

{-9, ∞}

Find the domain of the following function; give your answer in words, as an inequality and using interval notation:

In words: The domain of this function is all numbers greater than or equal to 1.

As an inequality: *x* ≥ 1

Using interval notation: {1, ∞}

The domain of a function is all the input values of that function - every number that could be placed in the function. The only numbers that cannot be part of the domain are those that make the function have a negative square root or a zero in the denominator of a fraction.

After learning about the domain in math, gauge how well you can:

- Characterize a function
- Highlight the relationship between a range and a domain of a function
- Determine the domain of a function through algebra or with a graph

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
13 in chapter 14 of the course:

Back To Course

ACT Prep: Help and Review44 chapters | 435 lessons | 26 flashcard sets

- What is a Function: Basics and Key Terms 7:57
- Inverse Functions 6:05
- Applying Function Operations Practice Problems 5:17
- How to Compose Functions 6:52
- How to Add, Subtract, Multiply and Divide Functions 6:43
- What Is Domain and Range in a Function? 8:32
- Functions: Identification, Notation & Practice Problems 9:24
- Compounding Functions and Graphing Functions of Functions 7:47
- Understanding and Graphing the Inverse Function 7:31
- Polynomial Functions: Properties and Factoring 7:45
- Polynomial Functions: Exponentials and Simplifying 7:45
- Algebraic Function: Definition & Examples 6:26
- Domain in Math: Definition & Overview
- Go to ACT Math - Functions: Help and Review

- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- U.S. Politics & Civics Lesson Plans
- US History - Civil War: Lesson Plans & Resources
- Computer Science 321: Ethical Hacking
- Overview of Financial Mathematics
- Data Analysis in Math
- HSPT Test: Perimeter, Area & Volume
- HSPT Test: Verbal Reasoning
- Fashion Design Lesson Plans & Resources
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison
- TACHS Prep Product Comparison
- Top 50 Blended Learning High Schools
- EPPP Prep Product Comparison
- NMTA Prep Product Comparison
- Study.com NMTA Scholarship: Application Form & Information

- History of Sparta
- Realistic vs Optimistic Thinking
- How Language Reflects Culture & Affects Meaning
- Logical Thinking & Reasoning Questions: Lesson for Kids
- Health Awareness Activities
- Green Revolution Lesson Plan
- What is Port Scanning? - Definition, Types & Tools
- Quiz & Worksheet - Frontalis Muscle
- Octopus Diet: Quiz & Worksheet for Kids
- Quiz & Worksheet - Fezziwig in A Christmas Carol
- Quiz & Worksheet - Dolphin Mating & Reproduction
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- 4th Grade Math Worksheets & Printables
- ELA Lesson Plans

- MTEL Political Science/Political Philosophy (48): Practice & Study Guide
- MTTC Sociology (012): Practice & Study Guide
- Creating Proactive Customer Service
- Education 102: Literacy Instruction in the Elementary School
- The Giver Study Guide
- TExMaT Master Mathematics Teacher 8-12: Complex Numbers
- General Science: The Immune & Endocrine Systems
- Quiz & Worksheet - The Adjourning Stage of Group Development
- Quiz & Worksheet - Wordsworth's The Solitary Reaper
- Quiz & Worksheet - HR Planning Pros & Significance
- Quiz & Worksheet - Characteristics of Marketing Plans
- Quiz & Worksheet - Characteristics of B2B Marketing

- What is a Stacked Bar Chart?
- Citing a Website in APA
- Idaho Science Standards for 5th Grade
- Understanding TELPAS Scores
- Wisconsin State Teaching Standards
- Persuasive Writing Prompts: Middle School
- Teacher Retirement System of Texas Withdrawal
- Community Lesson Plan
- New Jersey Science Standards
- Alabama State Standards for Science
- Homeschooling in Wisconsin
- Colorado State Math Standards

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject