Is This Function ONE-to-ONE? (Horizontal Line Test Explained!)

Описание: In this short lesson, I explain why a graph that rises and falls cannot be one-to-one. Using the horizontal line test, we see that different x-values (like around 3 and 4.2) give the same output, which means the function fails the test and does not have an inverse. Great for algebra, precalculus, and early calculus students.

A function is one-to-one if distinct inputs always produce distinct outputs. In this video, I walk through that definition using a real example: a graph that increases, decreases, and clearly repeats outputs for different x-values. By drawing a horizontal line through the region between x ≈ 3 and x ≈ 4.2, we can see it intersects the graph more than once. That’s the horizontal line test in action—and it shows immediately that the function is NOT one-to-one.

Topics covered: 1) What “one-to-one” really means, 2) How to use the horizontal line test, 3) Why failing the test means no inverse function, and 4) Visual understanding instead of memorizing rules. This is a key idea in algebra, precalculus, and the foundations of calculus and inverse functions. The full explanation is available in the long-form video!'

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Is f ONE-to-ONE?? Definition of One-to-One and the HORIZONTAL LINE TEST

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