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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) = 1 + 3x^2 - x^4 $

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Even function.

00:28

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

Harvey Mudd College

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…

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Determine whether f is eve…

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Determine whether $f$ is e…

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So here we have a function f of X, and we want to determine if it's odd, even or neither. So remember that for odd functions, opposite X values have opposite. Why values? So the graphs will have origin, symmetry and for even functions. Opposite X values have the same y value, so the graphs will have y axis symmetry. So we went to find out what f of the opposite of exes and determine if it's the same as the original, the opposite or neither. So we substitute the opposite of X in for acts in our function, and we get one plus three times the opposite of X squared, minus the opposite of X to the fourth power. Now, when you're squaring or raising to the fourth, whether it's positive or negative, it's going to end up to be the same. So the opposite of X quantity squared is equivalent to X squared, and the opposite of X quantity to the fourth is equivalent to X to the fourth. So notice that what we have now looks exactly the same as what we started with. So that means that f of the opposite of X is equal to f of X, and that means that we haven't even function. So if we graph this, we should be seeing why. Access symmetry so we can grab a calculator. Type this in and graph, and there's a graph that does appear to have y axis symmetry.

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