10 ! full answer in step by step all parts a, b, c, d, e

The first thing to do is to get the graph. That's below. That is a very wicked looking graph. I'm not sure what happens at 0. I'm not sure it is continuous at 0. That's something to make a fuss over because x = 0  is one of the x intercepts.

y = - x^(2/5)(x(5/5) + 7).
y = - x^(2/5)(x + 7)
So one of the x intercepts is 0 and the other one is -7.

The reasons are known because the factors can be equated to 0. It does not look to me like there is exact symmetry. There is a local minimum however at what the graph says is (-2,-6.5 or so)
You could differentiate that to find the exact point, but you are not asked for that.

So the domain is from -∞ to zero and 0 to plus ∞ I think you have to exclude 0 even though it is an x intercept. 

The graph decreases from -∞ < x < -2
It increases from -2 < x < 0
It decreases form 0< x < ∞