Question

How to determine if a function is even or odd calculus?

Answer 1

A function $f(x)$ is even if $f(-x)=f(x)$, and is odd if $f(-x)=-f(x)$.

Example:

$f(x)=x^2$ is even, since $f(-x)=(-x)^2=x^2=f(x)$.

$g(x)=x^3-x$ is odd, since $g(-x)=(-x)^3-(-x)=-x^3+x=-(x^3-x)=-g(x)$.