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.
The master cylinder is a hydraulic pump. As you pump the pedal, it forces the fluid into the calipers/wheel cylinders (or clutch bearing for a clutch master cylinder). This works really well because fluid does not compress. Air, however, compresses quite easily, so any air in the braking system will reduce the hydraulic pressure by large amounts.