The domain is all real values of x.
This is the equation of a parabola which opens upwards and has a minimum value . To find this minimum value we need to convert to vertex form.
x^2 + 8x + 17
= (x + 4)^2 - 16 + 17
= (x + 4)^2 + 1
Minimum value is 1
Range is y >= 1 or [1, ∞) in interval form.
