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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.

00:43

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. Every X value can have only one y value, and every y value can have only one X value for every X value. To have only one y value means it's going to pass the vertical line test so you pass a vertical line through the function and it can only pass through one point, not more than one. So, yes, this one does pass the vertical line test, and for every Y value to have only one X value, it must pass the horizontal line test. So if you pass a horizontal line through, it can only pass through one point, not more than one. It does also pass the horizontal line test, so every X value has only one. Why value and every y value has only one X value. So, yes, this is a function, a 1 to 1 function

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