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.
Brake boosters are used only on power brakes, not manual brakes. The booster's function is to give more braking power with minimal pressure on the brake pedal. If the booster is not working properly, you will still have brakes, but the brake pedal will be very hard to push. A brake booster is what gives power brakes their power. It works on vacuum from the engine. The booster pushes on the master cylinder with the pressure applied to the booster by stepping on the brake. If the engine is off, it cannot get vacuum, therefore the brakes will be hard when the engine is off.