for a function of x:

the domain is the set of x-values for with the function is defined.

the range is the set of y-values for which the function is defined.

it is often easier to find the values for which a function is not defined, and say the domain or range is everything but that

with polynomials though, our lives are easy. polynomials are defined for all real x (unless we are restricting the domain with some additional condition).

for an even polynomial where the leading coefficient is positive, the range is