What is the primary function of the kernel in an operating system?

The primary function of the kernel in an operating system is to provide core services for other parts of the operating system. The kernel acts as a bridge between applications and the hardware of the computer, managing system resources such as the CPU, memory, and input/output devices. It is responsible for executing processes, managing memory allocation, and handling system calls from user applications. By providing these essential services, the kernel ensures that applications can operate smoothly and efficiently, coordinating their access to the underlying hardware without needing to manage those details themselves.

In this context, options such as providing a graphical user interface or handling user applications directly do not align with the kernel's central role. Instead, those functions are typically managed by higher-level components of the operating system. Similarly, while managing network connections can involve kernel-level components, it is primarily considered one aspect of the broader suite of services the kernel provides and is not its primary function. Hence, the correct answer emphasizes the kernel's foundational role in enabling the operating system to function effectively.