Which API facilitates dynamic visualization exploration through external services?

The Analytics Extensions API is the correct answer because it is specifically designed to enable dynamic visualization exploration and integration of external analytic services within Tableau. This API allows developers to create and integrate tools that extend Tableau's analytical capabilities, enabling interactions that are tailored based on real-time data analysis or external inputs. By using this API, users can leverage external services to enhance their visualizations and gain deeper insights into their data, creating a more interactive and exploratory data experience.

In contrast, the other APIs serve different purposes. The Metadata API focuses on providing detailed information about the Tableau Server metadata, such as data sources and their structure, which is valuable for data governance and understanding data lineage but does not facilitate dynamic visual exploration. The Hyper API is primarily used for working with Tableau's Hyper data engine, allowing the creation, modification, and management of Hyper files, which are optimized for fast data processing but do not directly support dynamic visualization capabilities. The Webhooks API, on the other hand, is utilized for sending notifications about events that occur within Tableau Server or Tableau Online, which can be useful for automation but is not designed for facilitating an interactive analysis experience.