Step-by-step explanation:
the degree of f(x) is at least 8.
a squared function has 1 turning point.
a cubic function has 2 turning points.
and so on.
under certain circumstances some turning points or also zero points can merge into the same point.
formally they all count separately, but practically they are the same.
so, when we can SEE 7 turning points, there must be at least a degree of 8 or more.
a function with lower degree can never "create" additional turning points.