You can describe the domain by every possible x value in the function, since that function has a vertical intersection line which means the x value will never pass it on the negative side, the domain would be from -2 to all the postive numbers, X > -2 or (-2,∞).
For the range, simply it's all the possible y values. In that function it's impossible to go under 0 or negative value. That means the range would be Y>0 or (0,∞).
If you want to know if it's a function or not you could try the vertical line test, select any x value and draw straight line on it, if the line crosses 2 y points in the same x value it wont be a function, In your case each x value has it's own Y value.
So the answer is Domain x>-2; Range y>0; Yes, it is a function