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Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function.

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Not a function of $x$

00:47

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 1

Four Ways to Represent a Function

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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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here we have this stair step looking graph, and we want to know if it's a function. So remember that to be a function, every X value could have no more than one y value. And so when you're looking at the graph, you can try the vertical line test, and when you pass a vertical line through, it can only pass through one point. There are plenty of vertical lines that can pass through that only passed through one point. However, there are places where if I pass a vertical line through, it passes through multiple points, and so this is not a function.

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