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A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

$f(x)$ is a one-to-one function.

00:44

Jeffrey P.

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

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we're deciding whether or not this function is 1 to 1. And to be 1 to 1 means that every X value has only one y value. And every y value has only one X value. And to test that every X value has only one y value. We do the vertical line test. So if you pass a vertical line through, it can only pass through one point, not more than one. So we can see that this does pass the vertical line test to see if every y value has only one X value. We test it with the horizontal line test pass a horizontal line through. And if it passes through only one point, not more than one, then it passes. Yes, this also passes that test, so that shows us that every X value has only one y value and every y value has only one X value. So, yes, this is a 1 to 1 function

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