Hi @Sumeetha Mogasati ,
Thanks for posting your question in Q&A forum.
If the 3rd party Function app is running on Consumption or Premium SKU, then the outbound IP address of the function app would keep changing and there is no other way apart from whitelisting the entire data center Ip addresses at the Azure app. If the 3rd party function app is moved to Dedicated app service plan SKU, then there would be static outbound IP addresses which would solve your problem.
Azure APIM will not be helpful in this scenario as you can restrict IP addresses using policy in APIM but not whitelisting. Maybe you can have a load balancer such as Azure front door in front of Azure app however you will still have to whitelist the function's data center IP addresses in the Azure front door and then send request to the Azure app.
So either you will have to whitelist the data center IP addresses or move the 3rd party function app to dedicated app service plan. It is unfortunate.
Hope this helps! Feel free to reach out to me if you have any queries or concerns.
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