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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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00:51

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

Idaho State University

Boston College

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.

12:15

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 …

04:07

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 so, if every X value has only one y value, it's going to pass the vertical line test. If you pass a vertical line through, it will pass through no more than one point. So, yes, this one does pass the vertical line test 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, will it pass through one point and not more than one? Well, some of them do, but then there are others that pass through multiple points. So this fails a horizontal line test. That means this is not a 1 to 1 function

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