Functions are all around us, disguised as actions on concrete objects. Composition of functions, too, is all around us, because these actions can be performed in succession, the output of one serving as the input for the next. In terms of Gray and Tall's (2001) "embodied objects" or Lakoff and Nunez's (2000) "mathematical idea analysis," this "embodied scheme" of action on objects may serve as intuitive grounding for the function concept. However, as Gray, Tall, and their colleagues have shown, such embodied schemes can also lead to serious "epistemological obstacles" in later stages of concept development. In the same vein, our own data show that the intuitions about change and invariance entailed by the action-on-objects scheme, although helpful in earlier stages of learning functions, may later come to clash with the formal concepts of function and of composition of functions. (Contains 7 tables and 18 footnotes.)