The function f(x) = (x - a)^3 represents a cubic polynomial, where a is a constant. This function describes how the output f(x) changes as the input x varies. The term (x - a) indicates that the function is shifted horizontally by a units. The cube of this term means that the function will have a characteristic "S" shape, with one inflection point at x = a . As x moves away from a , the values of f(x) increase or decrease rapidly due to the cubic nature of the function. For values of x less than a , f(x) will be negative, and for values greater than a , f(x) will be positive. This behavior makes f(x) = (x - a)^3 useful in various