C (although it is neither increasing nor decreasing at x = 0)
All the other ones are decreasing for part of the domain.
You posted this in the pre-calculus forum.
Thus there is no way to prove this one way or the other.
You can simply draw the graphs and see the answer. But that is hardly a poof.
On the other hand, with calculus we can see which one has a non-negative derivative. That would prove it.
Assigning a value to x has no indication of whether a function is increasing or not.
Why don't you just graph the function? To rigorously prove it, we note that its derivative is 9x^2, which is always non-negative. Therefore the function in (C) is always increasing (except when x = 0, where the derivative is zero).
Technically the function is increasing everywhere.
The the statement that is an increasing function means that if then .
That is clearly true in this case. When I made the remark reply #3 about proof, it was addressing the fact that this is a precalculus forum.
There is of course a perfectly good way of proving this.
Suppose that then then . Proved.