It you want to know all the functions of a operating system, I must say it depends on the operating system.
The functions that all operating systems have in common is the subroutines to perform input output operations, the ability to input a task to be performed, the ability to load the software to perform the task desired.
Most operating systems, but not all, include a way to terminate a task and provide job completion status (normal termination, abort, or return code).
Multi-task operating systems and multi-processor operating system all include a program to controls maximum uninterrupted time in the CPU providing preemption if required, job scheduler, and interrupt system. These operating systems almost always also include a memory management system for moving a program out of memory when it is preempted or an input output operation is desired and the program that is next in the scheduler requires some or all of the memory used by the program that was removed from memory.
Most, but not all, provide a file management system, provide a method for submitting user input, and in recent years provide some form of security and user rights to programs and/or data.
Beyond this most of features are just to optimize the ones indicated above such as allowing for task prioritization in the scheduler queue.
Though Microsoft has included such features as Internet Explorer in its operating system, that is NOT an operating system function.
In its most basic for, all an operating system is designed to do is provide an interface between the user and the machine and provide basic software that must exist to run jobs. Operating systems were originally created to save having to rewrite how to start a job, how to do input output operations, and how to determine job completion status. Previously every program had to include these abilities. Originally no one considered programs that were not supposed to terminate until the computer was physically destroyed (that is why some operating systems, now, do not include the capability to determine job completion status).