Refer to figure.
When the throttle is opened rapidly, the volume of air entering the engine increases almost instantaneously because air is a low-inertia fluid. Fuel, being a denser liquid, has higher inertia and tends to lag behind the airflow increase, creating a momentary lean condition in the mixture. This lean transient would cause the engine to hesitate, stumble, or even cut out momentarily on rapid throttle application. 

The accelerator pump is a small mechanically-driven pump linked directly to the throttle mechanism within the carburettor. When the throttle is opened quickly, the pump is mechanically actuated and injects an additional measured shot of fuel directly into the venturi throat or immediately downstream of it. This supplementary fuel charge compensates for the transient lean condition caused by the fuel-air inertia mismatch and ensures smooth and immediate engine response to rapid throttle inputs. 

The accelerator pump only functions during rapid throttle movements and has no effect during steady throttle settings or slow throttle changes where normal metering keeps pace with airflow.

Discharge additional fuel into the venturi → CORRECT. The accelerator pump injects an additional shot of fuel into the venturi throat of the carburettor when the throttle is rapidly advanced. This supplements the normal fuel metering during the transient period when air flow has increased faster than the fuel metering system can respond, preventing the mixture from going momentarily lean and ensuring smooth throttle response.

Enrich the mixture by allowing more air into the venturi → INCORRECT. Allowing more air into the venturi would lean the mixture, not enrich it, because more air with the same fuel flow produces a leaner ratio. Additionally the accelerator pump does not control air flow. It is a fuel injection device that adds extra fuel to compensate for the transient lean condition. 

Decrease the volume of air entering the venturi → INCORRECT. The accelerator pump has no mechanism to restrict airflow. It is a small fuel pump mechanically coupled to the throttle linkage. Restricting air entering the venturi is the function of the throttle butterfly valve, not the accelerator pump. 

Discharge additional fuel into the inlet manifold → INCORRECT. The accelerator pump discharges fuel into the venturi of the carburettor, not into the inlet manifold. Fuel injection into the manifold is a characteristic of fuel injection systems, which do not have carburettors. In a carburetted system, all fuel metering including the accelerator pump discharge occurs within the carburettor body at the venturi, upstream of the throttle and manifold.