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You can set up continuous deployment for Azure Functions from any branch of a GitHub repository. Unfortunately, the deployment system will either just deploy your files (Found solution 'D:\home\site\repository\src\Sample.sln' with no deployable projects. Deploying files instead.) or may try to deploy the wrong project (e.g., if you have a console app in your solution).

You can use a different branch in GitHub for the output of your solution, but this is awkward. The solution I chose is to deploy the Azure Functions App from a specific subfolder of a GitHub repository. You can do this by adding a .deployment file in the root of your repository that tells the deployment system where your Azure Functions App is. E.g.:

[config]
project = src/FunctionApp1

If you run into deployment errors like The "Move" task failed unexpectedly. (System.Runtime.InteropServices.COMException (0x800700A1): The specified path is invalid.) when the _GenerateFunctionsPostBuild target tries to copy your project output, then ensure you’re using v1.0.1 or later of Microsoft.NET.Sdk.Functions.