Back To Course

Math 105: Precalculus Algebra14 chapters | 124 lessons | 12 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn what makes a one-to-one function different from a regular function. Learn a simple test you can use to check whether a function is one-to-one or not.

A good way of describing a **function** is to say that it gives you an output for a given input. You give functions a certain value to begin with and they do their thing on the value, and then they give you the answer. For example, the function *f(x)* = *x* + 1 adds 1 to any value you feed it. You give it a 5, this function will give you a 6: *f*(5) = 5 + 1 = 6.

Functions do have a criterion they have to meet, though. And that is the *x* value, or the input, cannot be linked to more than one output or answer. In other words, you cannot feed the function one value and end up with two different answers. For example, if you give a supposed function a 1 and it gives you a 4 and a 10, then you know that this supposed function is not a real function. A real function would give you one solid answer only.

Now, let's talk about one-to-one functions. A **one-to-one function** is a function in which the answers never repeat. A normal function can have two different input values that produce the same answer, but a one-to-one function does not. For example, the function *f(x)* = *x*^2 is not a one-to-one function because it produces 4 as the answer when you input both a 2 and a -2, but the function *f(x)* = *x* - 3 is a one-to-one function because it produces a different answer for every input.

We can learn a lot by comparing graphs of functions that are and are not one-to-one functions. Let's look at one that is and one that is not a one-to-one function.

The function shown here is *f(x)* = *x* + 2, and it is a one-to-one function.

You can see that every input, *x*, produces a different answer, *y*.

Now, let's look at the graph of *f(x)* = *x*^2, which is not a one-to-one function.

This function is not a one-to-one function because we have two different input values, *x*, that produce the same answer, *y*. Look at the graph when the input is both a 3 and a -3. You can see that both produce 9 as the answer.

By comparing these two graphs, we can see that the horizontal line test works very well as an easy test to see if a function is one-to-one or not. The horizontal line test tells us that if you draw a line and the graph crosses the horizontal more than once, then the function is not a one-to-one function.

Looking at our second graph of *f(x)* = *x*^2, we see that if we draw a horizontal line, our graph crosses that line twice, which is more than once. Because our graph crosses the horizontal line more than once, we see that this function is not a one-to-one function.

What have we learned? We've learned that a **function** gives you an output for a given input. A **one-to-one function** is a function of which the answers never repeat. For example, the function *f(x)* = *x* + 1 is a one-to-one function because it produces a different answer for every input. The function *f(x)* = *x*^2, on the other hand, is not a one-to-one function because it gives you the same answer for more than one input. This particular function gives you 9 when you give it either a 3 or a -3. A one-to-one function would not give you the same answer for both inputs.

An easy way to test whether a function is one-to-one or not is to apply the horizontal line test to its graph. If the graph crosses the horizontal line more than once, then the function is not a one-to-one function.

As you go through this lesson, you can prepare to:

- Understand what constitutes a function
- Compare graphs
- Contrast functions and one-to-one functions
- Use the horizontal line test to determine whether a function is a one-to-one function

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
8 in chapter 10 of the course:

Back To Course

Math 105: Precalculus Algebra14 chapters | 124 lessons | 12 flashcard sets

- How to Add, Subtract, Multiply and Divide Functions 6:43
- How to Compose Functions 6:52
- Applying Function Operations Practice Problems 5:17
- Compounding Functions and Graphing Functions of Functions 7:47
- Domain & Range of Composite Functions: Definition & Examples 5:58
- Inverse Functions 6:05
- Understanding and Graphing the Inverse Function 7:31
- One-to-One Functions: Definitions and Examples 4:11
- One-Sided Limits and Continuity 4:33
- Function Application for the Real World 5:36
- Using Quadratic Formulas in Real Life Situations 5:22
- Go to Function Operations

- Computer Science 335: Mobile Forensics
- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- U.S. Politics & Civics Lesson Plans
- US History - Civil War: Lesson Plans & Resources
- HESI Admission Assessment Exam: Factors & Multiples
- HESI Admission Assessment Exam: Probability, Ratios & Proportions
- HESI Admission Assessment Exam: 3D Shapes
- HESI Admission Assessment Exam: Punctuation
- HESI Admission Assessment Exam: Linear Equations, Inequalities & Functions
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison
- TACHS Prep Product Comparison
- Top 50 Blended Learning High Schools
- EPPP Prep Product Comparison

- History of Sparta
- Realistic vs Optimistic Thinking
- How Language Reflects Culture & Affects Meaning
- Logical Thinking & Reasoning Questions: Lesson for Kids
- Exceptions to the Octet Rule in Chemistry
- Database Hacking: Attack Types & Defenses
- Pride and Prejudice Discussion Questions
- Quiz & Worksheet - Frontalis Muscle
- Quiz & Worksheet - Dolphin Mating & Reproduction
- Octopus Diet: Quiz & Worksheet for Kids
- Quiz & Worksheet - Fezziwig in A Christmas Carol
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- 10th Grade Math Worksheets & Printables
- ESL Games for the Classroom

- Virginia SOL - World Geography: Test Prep & Practice
- AP English Literature Textbook
- FTCE Mathematics 6-12 (026): Practice & Study Guide
- UExcel Contemporary Mathematics: Study Guide & Test Prep
- Praxis Middle School English Language Arts (5047): Practice & Study Guide
- MTEL Business: Accounting Cycle
- The Medieval Period - MTEL Political Science/Political Philosophy
- Quiz & Worksheet - Veterinary-Client-Patient Relationship
- Quiz & Worksheet - Functions of Marketing Management
- Quiz & Worksheet - Julius Caesar's Personality
- Quiz & Worksheet - 1970s Black Leaders
- Quiz & Worksheet - Characteristics of Series Circuits

- Employee Scheduling: Methods & Issues
- Overview of European Geography
- GMAT Test Dates
- Homeschooling in North Dakota
- Scholarships for Homeschoolers
- DNA Experiments for Kids
- How Can I Improve My ACT Scores?
- Manifest Destiny Lesson Plan
- Illinois Real Estate Licensing & Continuing Education
- Wisconsin Science Standards for First Grade
- Mexican-American War Lesson Plan
- Kentucky Homeschool Laws

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

Browse by subject