Which of the following is responsible for managing a website's database and server-side functionality?

The component responsible for managing a website's database and server-side functionality is typically the backend or server-side programming environment. This includes technologies such as:

1. Web Servers: These serve web pages to the requests made by users. Examples include Apache and Nginx.
2. Database Management Systems (DBMS): These manage the database where data is stored and retrieved. Examples include MySQL, PostgreSQL, and MongoDB.
3. Server-Side Languages: These languages are used to create the logic that runs on the server, interacting with the database and generating dynamic content. Common examples are PHP, Python, Ruby, and Node.js.

In summary, the backend is a critical part of web development that handles everything from database queries to web server interactions, playing a crucial role in the functionality of a website.