The domain is without restriction so x=(-oo, +oo)
The range has a minimum because this is a second order equation with a constant positive acceleration.
The minimum can be seen easiest by putting the equation into vertex form
y=x^2+2x-1
y+1=x^2+2x
y+1+1=x^2+2x+1
y+2=(x+1)^2
y=(x+1)^2-2 so the vertex is at the point (-1, -2), and this is the absolute minimum value for y or the range. As x approaches positive or negative infinity, y approaches positive infinity:
y=range=[-2, +oo)
