Why is the minimum degree of this function 5? How come the minimum of this function isn't 3? I understand that the number of turns usually gives the degree of the function. But, I was told that the number of roots is the MINIMUM degree.
This is a little tricky.....since we have 4 identifiable turning points, the degree of the polynomial will be one greater = 5
If we didn't have two intermediate turning points occuring between two roots, the degree would be 3
Note that the function x^4 + 1 has no real roots, but a degree of 4...so....we cannot solely rely on the roots to give us the degree.......also....it only has one turning point.....so.....we can't always rely on that to tell us anything about the degree either!!!!