# What does it mean for a function to be even odd or neither?

Space and AstronomyIf we get an expression that is equivalent to f(x), we have an even function; if we get an expression that is equivalent to -f(x), we have an odd function; and if neither happens, it is neither!

## How do you know if a function is odd or even or neither?

Answer: For an even function, f(-x) = f(x), for all x, for an odd function f(-x) = -f(x), for all x. If f(x) ≠ f(−x) and −f(x) ≠ f(−x) for some values of x, then f is neither even nor odd.

## What does it mean when a function is neither even or odd?

Video quote: *When is a function neither even nor odd. It's going to be neither if you plug in negative x. And if you do not get negative f of X. So what does that mean. Well let's say if you replace X with*

## What is an even function?

Definition of even function

: **a function such that f(x)=f(−x) where the value remains unchanged if the sign of the independent variable is reversed**.

## What is an example of an even function?

Even functions are those functions in calculus which are the same for +ve x-axis and -ve x-axis, or graphically, symmetric about the y-axis. It is represented as f(x) = f(-x) for all x. Few examples of even functions are **x ^{4}, cos x, y = x^{2}**, etc.

## What is a odd function?

Definition of odd function

: a function such that f (−x) =−f (x) where the sign is reversed but the absolute value remains the same if the sign of the independent variable is reversed.

## What is an odd function equation?

A function is odd if **−f(x) = f(−x), for all x**. The graph of an odd function will be symmetrical about the origin. For example, f(x) = x^{3} is odd. That is, the function on one side of x-axis is sign inverted with respect to the other side or graphically, symmetric about the origin.

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