Final answer:
Behavior analysts mean by the word 'function' the purpose of a behavior, specifically how it aids an organism in survival and reproduction within its environment, rooted in functional psychology.
Step-by-step explanation:
When behavior analysts use the term function, they are referring to the purpose of a behavior. This concept is rooted in the foundational theory of functional psychology, which arose from the work of figures like William James, John Dewey, and Charles Sanders Peirce. These psychologists integrated Charles Darwin's theory of evolution by natural selection into their understanding of psychology, leading to the view that behaviors are adaptive responses that have evolved to help organisms survive and reproduce in their environments. As such, a behavior's 'function' is its role in aiding an organism to thrive within its ecological niche.
In contrast, while mathematical and economic contexts also use the term 'function,' in those disciplines, it usually refers to a mathematical operation used in graphing or a part of a model that describes cause and effect relationships. However, this mathematical sense of the word 'function' is not what behavior analysts are referring to when they talk about the function of a behavior.