How to plot f(x) and f(y) nicely on the same plot

I'd like to plot y=-1,x=-1,x=y,x=y-y^3 and x=y^(1/2)-1 all on the same plot. I'd also like to be able to rotate the axis so that I can have X or Y being the vertical axis.

I've tried the following:
x = -2:0.01:2; Not sure how to set an appropriate range?
x = -1 ; x1 = y-y.^3 ; x2 = y.^(1/2) - 1;

But I can't get it to show y=-1...

Also one of my lines has a weird fuzzy color...