Final answer:
If a zero has an extremely high multiplicity, it will affect the function's behavior depending on whether the multiplicity is odd or even.
Step-by-step explanation:
If a zero has an extremely high multiplicity, it means that the zero appears many times as a root of the function.
In this case, the function will behave differently depending on whether the multiplicity is odd or even.
If the multiplicity is odd, the function will cross the x-axis at the zero.
For example, if the zero has a multiplicity of 3, the function will touch the x-axis at that point.
If the multiplicity is even, the function will touch the x-axis but not cross it. For example, if the zero has a multiplicity of 4, the function will touch the x-axis and then turn back.