We have gubernatorial for governors, senatorial for senators, mayoral for mayors; what is the adjective for “of or pertaining to a representative”? The word representational means something totally different. I don’t find representatal as a word. Nor represental. Congressional refers to both senators and representatives. Have we nothing specific? That seems like a pretty big lacuna.
The United States Code,2 USC 5341, states:
Representational allowance for Members of House of Representatives (a) In general There is established for the House of Representatives a single allowance, to be known as the "Members' Representational Allowance", which shall be available to support the conduct of the official and representational duties of a Member or Member-elect of the House of Representatives with respect to the district from which the Member or Member-elect is elected.
So “representational duties” is a term in use.
The word Representative can be used both as a noun and as an adjective. You can see this in the definitions of the word in the online version of the Merriam Webster dictionary: [https://www.merriam-webster.com/dictionary/representative]
In its constitutional usage, the word is used because the members of the House of Representatives are supposed to be elected to 'represent' the voters of a particular constituency. So these representatives speak for the people of that constituency just as a 'representative' of a local or national company, visiting someone's home, is 'representing' that company: what they tell you about it is in that sense adjectivally representative of the company (or political party) in question.
When, after being elected by their constituency, they speak and vote in the House, they sometimes act as representatives of their constituents on some particular individual issue or of the constituency as a whole on a broader legislative matter.
That does not make them necessarily 'representative' in the sense of typical of of their constituents. They might, for example, have been elected on a majority of 1%, where only 60% of the voters turned out to vote. They might not take any notice of problems raised with them by voters they suspect voted for the other side. But in that case, we could, I think, say that the Representative was failing in her/his representative duties, just as a mayor might in some respect fail in his/her 'mayoral' duties, or a governor fail in her/his 'gubernatorial' duties. More likely, though, is that they would be said to fail in their 'duties as a mayor', or 'duties as a governor' or 'duties as a representative'.