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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) = \dfrac{x^2}{x^4 + 1} $

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Even function

00:41

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

Missouri State University

Campbell University

Baylor University

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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here we have a function, and we want to determine if it's odd, even or neither. So remember that for odd functions, opposite X values give you opposite. Why values? And they have origin, symmetry and for even functions opposite X values give you the same y value. And so they have y axis symmetry. So what we want to do with this function is determined what we get when we plug in the opposite X value so f of the opposite of X. We're going to substitute the opposite of X in for acts in the function, and then we'll simplify. And the opposite of X squared is equivalent to X squared, and the opposite of X to the fourth is equivalent to X to the fourth. So are simplified version of EFT of negative X is equivalent to F of X that tells us that our function is even now we can go ahead and graph it on a graphing calculator and verify that by looking for the y axis symmetry. So we type it into our calculators y equals menu, and then we graph, and that does appear to have symmetry across the Y axis, so that confirms that it is even

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