Let's study the parity of $x^3-3$ with respect to $x$

The domain is $x\in ℝ$

This domain is symmetric about 0: if $x$ is in the domain, -$x$ is too

Replace $x$ by -$x$: f(-$x$) = ${(-x)}^3-3$

⇥Let's calculate: ${(-x)}^3-3$

⇥ⓘ Powers are computed before multiplications, additions and subtractions. With an even integer exponent, the minus sign in the base disappears; with an odd integer exponent, it moves in front of the power: ${(-x)}^3$ = $-x^3$

⇥ $-x^3-3$

f(-$x$) - f($x$) = $-2x^3$ and f(-$x$) + f($x$) = $-6$ are nonzero polynomials: the function is neither even nor odd

▶Parity: $\mathrm{neither\; even\; nor\; odd}$