Which service allows you to implement API gateways in Azure?

Azure API Management is the correct choice for implementing API gateways in Azure. This service provides a robust platform for creating, publishing, maintaining, and securing APIs at scale. It acts as a bridge between clients and backend services, allowing for effective management of API lifecycles.

Azure API Management offers several key features such as traffic management, security through authentication, throttling, caching, and analytics, which are essential for optimizing and monitoring API performance and usage. By utilizing this service, organizations can expose backend APIs securely and provide a unified endpoint for their various services, facilitating easier integration and interaction with applications.

In contrast, while Azure Logic Apps can automate workflows and connect apps and services, it's not specifically designed as an API gateway. Azure Functions is a serverless compute service that enables the execution of event-driven apps, but it does not provide the full suite of API management capabilities. Azure Service Bus is designed for message queuing and communication between different services, rather than for managing APIs directly. Thus, Azure API Management stands out as the dedicated solution for enabling and managing API gateways within the Azure ecosystem.