Hi @Pavan Puligandla ,
Welcome to the Microsoft Q&A Platform! Thank you for asking your question here.
Yes, App Gateway public IP will be used by external Clients to consume function app APIs. Please refer Integrate API Management in an internal virtual network with Application Gateway for Application Gateway to APIM integration.
For APIM and Function app integration, follow Import an Azure function app as an API in Azure API Management
Please let me know if any further information is needed or issue at any particular steps.
Architecture Reference: Protect APIs with Application Gateway and API Management