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Sketch the graph of the function.

$ f(x) = x + | x | $

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$|x|=\left\{\begin{array}{ll}x & \text { if } x \geq 0 \\ -x & \text { if } x<0\end{array}\right.$$f(x)=x+|x|=\left\{\begin{array}{ll}2 x & \text { if } x \geq 0 \\ 0 & \text { if } x<0\end{array}\right.$Graph the line $y=2 x$ for $x \geq 0$ and graph $y=0$ (the $x$ -axis) for $x<0$

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

Missouri State University

Campbell University

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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Sketch the graph of the fu…

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Sketch the graph of functi…

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he sketched the graft the functions So we have F equals X plus the absolute value of ax. And to start off we'LL start with the definition here for the absolute value of X equals positive X. If X is greater than equal, did it greater than or equal to zero and negative acts if excess less than her uh, X is less than zero. So if you're not convinced that this just take a moment and pause. Teo, convince yourself that this is true. Hey, and so f in this case is going to be either X plus X if X is greater than or equal to zero or it's going to be X minus sechs. Yeah, ex lesson tio continuing on Well, we get into getting two acts Yes, X rated R zero or it's going to be zero. Otherwise so to graft this So two X if X is greater than or equal to zero So well, I include zero here with, uh, two acts like that, and zero otherwise So I have school. Axe is legal. Wait, Did this graph dysfunction

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