Definition of a Function. A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair. Okay, that is a mouth full.
Master cylinder without booster. Single bore master cylinders: These unboosted hydraulic Master Cylinders are actuated by foot effort, via the brake pedal. The brake pressure is related to actuation force and depends on the piston bore size: the smaller the bore, the higher the pressure.
if you are talking about the brake master cylinder, if it goes bad you have no brakes. (or a clutch master cyl.....no clutch) the master cylinder is the part of the brake hydraulic system that the driver controls with the foot pedal.