Find the range for f(x) = x2 + 1, for x < 0. y ≥ 1 y > 1 y < 1 y ≤ 1

Here, you have to determine values of f(x) for negative domain. Domain are those values of x for which function is defined.
Since the function is a polynomial, every value of x∈R is defined for f(x).
And for every negative value of x, f(x) will always be positive because x is squared and square of  negative real number is always positive. 
0 is neither negative nor positive. Therefore, zero is not included in negative domain. If you plug say x= -0.00000956, f(x) will be greater than 1 because square of x will never be negative. 
Thus, the range will always be positive or greater than equal to 1. 
Therefore, y≥1