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]}