Azure Functions are hosted within Azure App Service, so they get all of its features. Diagnostic and monitoring logs can be configured easily using platform features. Furthermore, App Service provides options for assigning SSL certificates, using a custom domain, authentication, and authorization as part of it's networking features. 

Although customers are not concerned about the infrastructure, operating system, filesystem, and platform on which the Functions actually execute, Azure Functions provides the necessary tooling to peek within the underlying system and make changes. The console and the Kudu console are the tools used for this purpose. They provide a rich editor to author Azure Functions and edit their configuration.

Azure Functions, just like App Service, allow the storage of configuration information within the web.config application setting section, which can be read on demand: