Final answer:
Azure Monitor for containers is the service designed for monitoring the performance and health of container workloads, providing insights and alerts for Azure-based container environments.
Step-by-step explanation:
The service that is designed to monitor the performance of container workloads is A) Azure Monitor for containers. This tool provides capabilities for monitoring, visualizing, and alerting on container metrics and logs. It allows developers and system administrators to gain insights into their container workload's performance, ensuring they can proactively handle any issues that may arise with the health and availability of their applications hosted in Azure Kubernetes Service (AKS) and other containerized environments.