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Determine whether $ f $ is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually.

$ f(x) = x | x | $

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Odd function.

00:46

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

Johns Hopkins University

Missouri State University

University of Michigan - Ann Arbor

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.

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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Determine whether $f$ is e…

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Determine whether f is eve…

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Determine whether $ f $ is…

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all right. We want to determine if this function is even on or neither. And so remember that for odd functions, opposite X values have opposite. Why values? And so the grafts have origin, symmetry and for even functions opposite X values have the same y value. And so the grafts have y axis symmetry. So what we want to do is determine if f of the opposite of X is going to be the same as or the opposite of, or neither compared to f of X. So we substitute the opposite of X in the function, and we get the opposite of X times the absolute value of the opposite of X. Now realize that the absolute value of the opposite of X is just the same thing as the absolute value of X X, and the opposite will be the same distance from zero, so we can simplify it. Now that looks like the opposite of what we originally had. So we've just found that f of the opposite of X is equal to the opposite of F of X, which means this function is odd. Now we can grab it on a calculator and see the origin symmetry. So we type it into the calculator and we look at the graph and there you see that origin symmetry.

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