# Is the function f(x)= 6x^3 - 2x even, odd or neither?

Oct 20, 2015

It's odd.

#### Explanation:

A function is odd when $f \left(- x\right) = - f \left(x\right)$

$f \left(- x\right) = 6 {\left(- x\right)}^{3} - 2 \left(- x\right)$

$= - 6 {x}^{3} + 2 x$

$= - \left(6 {x}^{3} - 2 x\right)$

$= - f \left(x\right)$

Thus, the function is odd.

If a function is odd, then it is symmetric over the $x$-axis.

graph{6x^3-2x [-9.375, 10.625, -4.8, 5.2]}