Final answer:
The leading coefficient of a polynomial function determines the behavior of the function as the input values increase or decrease.
Step-by-step explanation:
The leading coefficient in a polynomial function determines the behavior of the function as the input values increase or decrease. It is the coefficient of the term with the highest degree in the polynomial. If the leading coefficient is positive the graph of the polynomial rises on the right side and falls on the left side.
This means that as the input values increase the output values also increase. Conversely, if the leading coefficient is negative the graph falls on the right side and rises on the left side. In this case as the input values increase the output values decrease.