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)
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.
Yes, we can make conclusions about the leading coefficient and degree of the polynomial function based on the given information about its range.
The range of the polynomial function is {y | y ≤ 5, y ∈ R}. This means that the highest value the function can take is 5, and it can take any value less than or equal to 5. Since the range is limited to values less than or equal to 5, we can conclude that the degree of the polynomial must be at most 1.
If the degree of the polynomial is 0, the function would be a constant function and would have a single value in its range. However, in this case, the range includes all values less than or equal to 5, so the degree of the polynomial cannot be 0.
Therefore, based on the given information, we can conclude that the degree of the polynomial function is 1 or higher. However, we cannot determine the exact degree or the leading coefficient without additional information.