📚 Learn How to Use the Horizontal Line Test to Identify One-to-One Functions! In this video, you’ll learn how to determine whether a function is one-to-one using the horizontal line test. We explain what it means for a function to be one-to-one both algebraically and graphically, and show you how to apply the horizontal line test to decide whether a function has an inverse.
By the end, you’ll understand how to identify one-to-one functions, how to restrict domains to make a function one-to-one, and how this connects to inverse functions.
🔍 What You’ll Learn in This Video:
✅ What Is a One-to-One Function?
✔ Each output corresponds to exactly one input
✔ If f(x₁) = f(x₂), then x₁ = x₂
✔ Why one-to-one functions are required to have an inverse
✅ What Is the Horizontal Line Test?
✔ A method to test whether a function is one-to-one
✔ If every horizontal line intersects the graph at most once, the function is one-to-one
✔ If a horizontal line hits the graph more than once, the function is not one-to-one
✅ How to Restrict the Domain to Make a Function One-to-One:
✔ Some functions (like f(x) = x²) are not one-to-one over their entire domain
✔ Restricting the domain (e.g., x ≥ 0) can make the function one-to-one
✔ Once restricted, the function can have an inverse
📊 Examples Covered in This Video:
✔ Graph of f(x) = x → Passes the horizontal line test
✔ Graph of f(x) = x² → Fails the test unless the domain is restricted
✔ How to test visually and algebraically for one-to-one behavior
By the end of this lesson, you'll be able to:
✔ Apply the horizontal line test to any graph
✔ Determine if a function has an inverse
✔ Make a function one-to-one by restricting its domain
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• How to Find the Average Rate of Change | S...
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• How to Analyze a Graph | Increasing, Decre...
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• Domain of a Composite Function | Step-by-S...
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• Transformations of Functions | Shifts, Str...
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Timestamps
00:00 Introduction
00:28 One-to-One Functions
03:26 The Horizontal Line Test
05:56 Restricting the Domain of a Function
More About Understand The Math
Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples.
Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective.
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