This is possible. If you just want to get a token from the user assigned identity to pass to other functions then this is answered here.
If you want to pass through user identity all the way down it is a bit more tricky. Apologies for the link heavy answer, this is a big topic and involves a number of steps to put in place. Hopefully this gives you all the keywords (on behalf of flow, server to server authentication and grant consent to applications) to find some good blog articles to walk you through.
You need to break the problem down in to pieces.
- Use Active Directory authentication for the first call. You either need to add the configuration in to your deployment scripts or manually configure the Azure Active Directory set up using the wizard/tools in the Azure Portal.
- Implement the "On behalf of" Authentication flow to run the downstream functions using the context of the user that was authenticated in the first call. This requires you to set up service to service authentication. A sticky point if often the "Grant Consent" that needs to be set up.
Picture from the docs
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Grant Consent
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