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.
A brake booster needs the right amount of vacuum to operate correctly. This is typically engine manifold vacuum (17-21Hg). On some engines, particularly diesels, an auxiliary pump is used to create vacuum. This vacuum is applied to both sides of the booster. Both the pedal side and the master cylinder side. As the driver presses the brake pedal, the vacuum valve blocks the vacuum source located on the pedal side of the booster. At the same time the air valve moves allowing atmospheric pressure in.