Uit ArchiMate:"Just like a business process, a business function also describes internal behavior performed by a business role. However, while a business process group’s behavior is based on a sequence or 'flow' of activities that is needed to realize a product or service, a business function typically groups behavior based on required business resources, skills, competences, knowledge, etc.
There is a potential many-to-many relation between business processes and business functions. Complex processes in general involve activities that offer various functions. In this sense a business process forms a string of business functions. In general, a business function delivers added value from a business point of view. Organizational units or applications may coincide with business functions due to their specific grouping of business activities.
A business function may be triggered by, or trigger, any other business behavior element (business event, business process, business function, or business interaction). A business function may access business objects. A business function may realize one or more business services and may use (internal) business services or application services. A business role or an application component may be assigned to a business function. The name of a business function should preferably be a verb ending with '-ing'; e.g., 'claims processing', or a noun ending in '-ion' or '-ment'; e.g., 'administration'."