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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.

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

00:43

Jeffrey Payo

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

Missouri State University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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A function is given by a t…

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A function is given by a …

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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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