Question

what is the domain and range of g(x)=x^2-5

Answer 1

for all polynomials, the domain is all reals...
for the range,all polynomial functions depend on the end behavior of the function: if the degree of the polynomial function is odd, the range is all reals; if the degree i even, then it either has a maximum or minimum....

in your case, the degree is even so it has a maximum or minimum and the range will depend on that value... you have a parabola and its maximum or minimum occur at the vertex.... find the vertex...