Does taking the derivative of a system of equations affect the range of those equations? I've never had to do this before, so just asking. (Example below.)

Question

mendicant_bias · Answer

$$g(x) = \left\{ x^3, -2\le x \le 0 \right\}$$$$g(x) =\left\{ x^2, 0<x \le 2 \right\}$$(Improper use of brackets, I know, but I can't write it the "proper" way yet with Openstudy.)
$$g'(x) = 3x ^{2}$$$$g'(x) = 2x$$Are the ranges of these at all affected?

anonymous · Answer

the ranges are not effected at all, what the original equation is stating is that it is restricting them to their respective domains.

mendicant_bias · Answer

Just making sure. I know what the original equation is stating, but I don't want to assume that continually holds true. Thanks.