What key function can members of the house of representatives perform that the delegates from the district of Columbia cannot

The correct answer is : A vote on legislation.

One of the greatest paradoxes of the District of Columbia is that is the center of power in which, by many, is considered the strongest democracy on the planet, but its residents have less rights that those who live in other states in the United States. The District of Columbia cannot determine its own budget, it does not have a delegate with vote on legislation in the Congress, and it cannot approve local laws in a definitive manner.

The main reason is that the country's Constitution established that in order to guarantee its security and function, the capital should not become a State, but a federal district under the jurisdiction of legislators, otherwise, if the capital as also a state it would have too much power.

District of Columbia residents have one member in the House of Representatives with no vote on legislation, as well as a small delegation (with no vote also) that advocates for their interests at the Senate of the United States. This delegate can only vote on procedural matters and in congressional committees.