Final answer:
The correct example of outsourcing an entire business function is paying another organization to handle employee travel arrangements, as it transfers a complete operational task to an external service provider.
Step-by-step explanation:
An example of outsourcing an entire business function is E: paying another organization to arrange for employee travel. Outsourcing involves contracting with an external organization to perform services or functions that were traditionally handled internally. This can range from IT services to human resources and in this case, the comprehensive management of employee travel arrangements. It is a strategic move for companies looking to cut costs by leveraging the specialization and economies of scale offered by external firms. In contrast, options such as acquiring technology, buying hardware, licensing software, and making software customizations do not constitute the outsourcing of an entire business function but are rather means to enhance efficiency within the company.