A cloud infrastructure function that can grow and shrink to meet peak demand requirements quickly is known as:

Elasticity in cloud computing refers to the ability of a system to quickly expand or decrease its resource capacity to meet fluctuating workloads. This dynamic scaling allows the infrastructure to provision and deprovision resources automatically based on demand, ensuring optimal performance during peak times and cost efficiency during low usage.

Federation typically refers to a system where multiple independent entities (like cloud providers or identity systems) operate together under a unified management, which is unrelated to dynamic resource scaling.

Automation involves using technology to perform tasks with minimal human intervention, and while it enables elasticity, it is not the term for the characteristic of growing and shrinking capacity itself.

Caching is a technique for storing frequently accessed data temporarily to speed up retrieval, which improves performance but does not describe the ability of the infrastructure to grow and shrink in capacity.