Determine whether the graph of the given function f(x) = 4x^3 is symmetric with respect to the y-axis, symmetric with respect to the origin, or neither.

f(x) = 4x^3

f(-x) = 4(-x)^3 = -4x^3 = -f(x)

So the f is symmetric with respect to the origin and "odd".

But f(-x) ≠ f(x) so f is not symmetric with respect to the y-axis so is not "even".

[N.B.: Any circle x^2 + y^2 = r^2 is symmetric to any line through the origin: it's even, odd, and its own inverse.]