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

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Answer 1 · 2015-10-20T04:00:32

It's odd.

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

$f(-x) = 6(-x)^3 - 2(-x)$

$=-6x^3+2x$

$= - ( 6x^3 -2x)$

$= - f(x)$

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]}

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