Since f(x) is linear we need only the lowest and highest values of the domain to determine the range.
f(-8)=(-3)(-8)+7=24+7=31; f(2)=(-3)(2)+7=-6+7=1 so the range is [1,31], if by range is meant the spread of f(x).
However, the range is usually considered to be the set of f(x) values corresponding to the set of domain values, so range={ 1,13,16,25,31 } the ordered set corresponding to { -8,-6,-3,-2,2 }.