After having published an Azure Function, you can monitor it in the following way. Consider that the host.json file can be modified in order to control the logging behavior.
See the Azure documentation to know how to set the host.json file.
First, access the Azure portal and select your function.
Click on the Monitor option on the left hand side:
There you can see all the invocations (successful or not) of the function.
And check the invocation details (if any error is thrown, it will be shown in this panel).
The logging information can be seen using the Logs tab in the Monitor panel.