Question

PLEASE EXPLAIN: h(x) = sqrt(4-x^2), find the domain and range.

Answer 1

H(x), or the range of this function, must be y >= 0, as you can never get a negative when square rooting any number.

For the domain, x cannot exceed -2 or 2, as this would mean we'd be finding the square root of a negative number, which can't happen without getting in to imaginary numbers. Thus, the domain must be -2 <= x <= 2.