Final answer:
The cell grows quickly and begins to carry out routine metabolic functions during the G1 phase of the cell cycle, which precedes DNA replication in the S phase.
Step-by-step explanation:
The phase of the cell cycle where the cell grows quickly and begins to carry out routine metabolic functions is known as the G1 phase or first growth phase. During G1 phase, cells increase in size and carry out normal activities essential for the cell's function. Furthermore, this phase is characterized by intense biosynthetic and metabolic activities, which include synthesizing amino acids and the proteins required for DNA replication. Upon completion of the G1 phase, cells that are set to divide proceed to the S phase, where DNA replication occurs in preparation for cell division.