(1) A system outcomes which contribute to goals or objectives. To have a function, a system must be able to provide the outcome through two or more different combinations of elemental behavior. (Ackoff 1971)
(2) An action, a task, or an activity performed to achieve a desired outcome. (Hitchins 2007)
(3) A broad work area encompassing multiple related disciplines (e.g., Engineering, Finance, Human Resources, etc.). (Created for SEBoK)
(4) A function is defined by the transformation of input flows to output flows, with defined performance. (Created for SEBoK)
(1) Ackoff, R.L. 1971. "Towards a System of Systems Concepts". Management Science. 17(11).
(2) Hitchins, D. 2007. Systems Engineering: A 21st Century Systems Methodology. Hoboken, NJ, USA: John Wiley & Sons.
(3) and (4) These definitions were developed for the SEBoK.
(1) is the system science definition. All systems have behavior, but to be able to function in a certain way they must have a certain richness of behavior. For example, fight, flight or hide are behaviors; while response to external threats is a function.
(2) is the more traditional Systems Engineering definition, in which functions are identified top down based on needs and then decomposed and allocated to lower level system.
(3) is a HW/SW or human system component definition, describing a function which can be performed by a single part of the system with identified performance.
(4) is a management definiton, describing how similar functions are collected in organizational units. SEBoK v. 1.9.1 released 16 October 2018