Final answer:
The appraisal function within the organization that offers a multitude of services to management is known as internal auditing. It is an independent and objective activity that aims to enhance the operations and processes of an organization.
Step-by-step explanation:
The appraisal function housed within the organization that performs a wide range of services for management is internal auditing. Internal auditing is an independent, objective assurance and consulting activity designed to add value and improve an organization's operations. It helps an organization accomplish its objectives by bringing a systematic, disciplined approach to evaluate and improve the effectiveness of risk management, control, and governance processes. Internal auditing is typically contrasted with external auditing, which is conducted by independent professionals outside the organization to assess the truth and fairness of financial records often for statutory or regulatory reasons.