A function field is a type of field in mathematics that consists of functions, typically defined over a certain base field, such as the field of rational numbers, ℚ. These fields are often used in algebraic geometry and number theory, where the elements are rational functions of one or more variables. Function fields can be thought of as extensions of the base field, where the elements are ratios of polynomials. For example, the field of rational functions in one variable over ℚ is denoted as ℚ(x), where x is an indeterminate. This concept helps mathematicians study properties of algebraic curves and their associated geometric structures.