Question

What are the domain and range of the real-valued function f ( x ) = − x 2 − 3?

Answer 1

Please, use " ^ " to denote exponentiation: f ( x ) = − x^2 − 3.

Since this is a polynomial, we can immediately state that the domain of f(x) is the set of all real numbers: (-infinity, infinity).

The maximum value of this function can be found by setting x = to 0:

y_max = -3. Thus, the range of this function is (-infinity, -3].