【Power】 ,  【faculty】 ,  【function】  can all mean an ability of a living being to act or perform in a given way or a capacity for a particular kind of action or performance.

【Power】 , the comprehensive term of this group, may apply to a capacity for action or performance that does not or apparently does not call the mind into play, but it more frequently applies to an ability or capacity that involves either mental activity or mental receptiveness.

【Faculty】 in general, as distinct from technical psychological or metaphysical use, is applicable to those powers which are the possession of every normal human being, though not always manifested in the first months of infancy or the earliest years of childhood or it may apply to any one of the several specific powers of the mind (as will, memory, and reason) that are often felt as discrete and discoverable.

Sometimes  【faculty】 means no more than a distinguishable capacity of the functioning mind or soul.

【Function】 may denote an activity which can be more or less definitely associated with the brain or the central nervous system or a part of either or it may apply to one (as digestion or respiration) in which the mental component is slight or obscure.