Adverb particles allow changes in verb meaning.
Don’t give up your race!
« up » is an adverbial particle (or postposition). This particle changes the meaning of a verb.
«To give» has the meaning of «to offer» while «to give up» means «to abandon».
«Your race» is a complement. It can be placed between the verb and the adverbial particle :
Don’t give your race up.
The main particles are: about, across, along, around, away, back, down, in, off, on, out, over, through, up.
List of phrasal verbs (non-exhaustive list):