Question

Given that the range of a polynomial function is {y | y <= 5, y ER}, do you have enough
information to make any conclusions about the leading coefficient or degree?


(er is all real numbers)

Answer 1

Since y has an absolute maximum, it must be of even degree, since all the odd-degree polynomials go forever in each direction.

And, its leading coefficient must be negative, since the graph opens downward.