How are translations represented as a function?

Translations can be represented as a function by defining a mapping that shifts each point in a geometric figure by a fixed distance in a specified direction. Mathematically, if ( f(x) ) represents a point in the plane, a translation by a vector ( (a, b) ) can be expressed as ( f'(x) = f(x) + (a, b) ). This means that for each point ( (x, y) ), the new point after translation will be ( (x + a, y + b) ). Thus, the translation function takes points from their original positions to their new locations based on the vector provided.