Consider the function q:R→[0,∞) given by q(x)=x2+4x+5.
(a) Rewrite q(x) in the completed-square form.
(b) Determine the minimum value attained by q on R and the point at which it occurs.
(c) Decide whether q is onto with respect to the stated codomain [0,∞). Provide a rigorous justification.
(d) Suggest the smallest interval that can serve as codomain so that q becomes onto, and verify your claim.