Which category of triage encompasses clients with serious health problems that are not immediately life threatening?

The answer is Urgent.

Fast track patients require simple first aid or basic primary care and may be treated in the ED or safely referred to a clinic or physician's office. Urgent patients have serious health problems that are not immediately life threatening. They must be seen within 1 hour. Emergent patients have the highest priority, their conditions are life threatening and they must be seen immediately.  Nonurgent patients have episodic illness that can be addressed within 24 hours without increased morbidity

b.have there own function.