What characteristic does a polynomial function have?

A polynomial function is defined as a mathematical expression that involves sums and non-negative integer powers of variables. The correct choice highlights that polynomial functions include curves, which arise from the varying degrees of their terms, but do not possess asymptotes. Unlike rational functions that can have asymptotes due to division by zero or behavior at infinity, polynomial functions are defined for all real numbers and exhibit continuity throughout their domain.

This characteristic is essential as it differentiates polynomials from other types of functions that might exhibit asymptotic behavior, such as rational and exponential functions. Because polynomials are made up of terms like (ax^n) where (n) is a non-negative integer, they can represent a range of behaviors depending on the degree of the polynomial, but they will not suddenly approach a line that they get ever closer to without touching (as asymptotes do).

In summary, option B correctly identifies the hallmark of polynomial functions: they include curves and do not have asymptotes, making them continuous and defined for all inputs within the real number system.