Question

Give an example of an odd function and explain algebraically why it is odd.

Answer 1

An odd function is a function of a form $y=x^n$ where n is an odd number.

Some examples would be functions:

$y=x,y=x^3,\dots$.

A formal definition of odd function is the following.

(Algebraic proof).

Let $f:\mathbb{R}\to\mathbb{R}$ (real function).

The function is odd if the below equation is true for all x and -x for which the function is defined:

$f(x)=-f(-x)$.

Hope this helps.