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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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00:44

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

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

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 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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