Deploying a function in an App Service Environment is the primary way to have static inbound and outbound IP addresses for your functions. For details on using an App Service Environment, start with the article Create and use an internal load balancer with an App Service Environment.
You can also use a virtual network NAT gateway to route outbound traffic through a public IP address that you control. To learn more, see Tutorial: Control Azure Functions outbound IP with an Azure virtual network NAT gateway.