Since x is the exponent of 0.25, it does not have restrictions. Therefore the domain is R. In interval notation that is (-infinity,infinity).
Since x can be any real number, y will only be positive (natural numbers). When x is negative, y < 1 but never 0 since there is no value of x that makes 0.25^x = 0. Also, when x is 0 or positive, y ⩾ 1. Therefore, the range is N (set of positive numbers).