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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) = 2x - 3 $

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yes $(1$ to 1$)$

00:39

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

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

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.

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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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02:12

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. Why value and every y value has only one X value. So we can visualize this one, since we know is just a graph of the line with the Y intercept of negative three and a slope of two. So it looks roughly like this. So for every y value to have only one X value, it must pass the horizontal line test. If you pass a horizontal line through, it will go through no more than one point. So that's a pass. And for every X value to have Onley one y value, it must pass the vertical line test pass a vertical line through and it only goes through one point, not more than one. And that's a pass. So, yes, this one is 1 to 1

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