Find the end behavior of y=2x(x-1)(x+1):
This is a cubic polynomial with positive leading coefficient. (You can write in standard form: y=2x(x+1)(x-1) ==> `y=2x(x^2-1)`
==>`y=2x^3-2x` The leading coefficient is 2.
A cubic with positive leading coefficient has the following end behavior:
As `x->-oo,y->-oo` and as `x->oo,y->oo` .
(As x decreases without bound, y decreases without bound; as x increases without bound, y increases without bound.)
(Note that the function is odd -- there is rotational symmetry of 180 degrees about the origin.)
The zeros of f(x) is 0,1 and -1.
Thus function has three zeros.
Thus by def of odd function. f(x) is an odd function.