Let's study the parity of $8x^3+3x$ 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(-$x$) = $8·{(-x)}^3+3·(-x)$

⇥Let's evaluate: $8·{(-x)}^3+3·(-x)$

⇥ⓘ 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: ${(-x)}^3$ = $-x^3$■The minus sign is placed in front of the product: $3·(-x)$ = $-3x$

⇥ $8·(-x^3)-3x$

⇥ⓘ The minus sign is placed in front of the product: $8·(-x^3)$ = $-8x^3$

⇥ $-8x^3-3x$

f(-$x$) = -f($x$): the function is odd

▶Parity: $\mathrm{odd}$