Power series allow us to represent associated functions on an appropriate interval. Represent a function at a point as a Taylor polynomial. The coefficient of the nth degree term in a Taylor polynomial for a function f centered at x = a is f^n (a)/n!.In many cases, as the degree of a Taylor polynomial increases, the nth degree polynomial will approach the original function over some interval. Approximate function values using a Taylor polynomial. Taylor polynomials for a function f centered at x = a can be used to approximate function values of f near x = a.