A find the domain and range and state the answer in

Question

For the function:

f (x) = { x², x > 0 { -x², x < 0

a.) Find the domain and range and state the answer in Interval Notation

b.) Find the mathematical formula for f (x) WITHOUT the use of the Heaviside function

If you could give basic explanations for each step, so I can practice and see how you got the answer, that would be greatly appreciated!