The functionality of a monomeric structural unit is defined as the number of covalent bonds which it forms with other reactants.
Unless the macromolecule is cyclic, it will have monovalent structural units at each end of the polymer chain.
For example, in the synthesis of PET, a small fraction of the ethylene glycol can be replaced by glycerol which has three alcohol groups.
This trifunctional molecule inserts itself in the polymeric chain and bonds to three carboxylic acid groups forming a branch point.
For example, in the synthesis of cross-linked polystyrene, a small fraction of monomeric styrene (or vinylbenzene) is replaced by 1,4-divinylbenzene (or para-divinylbenzene).