Want to upgrade vertica from 7.0 to 9.3.

One easy way is to just build a new cluster and migrate the data across. If that's not an option, you'll need to follow the upgrade paths: https://www.vertica.com/docs/8.1.x/HTML/index.htm#Authoring/InstallationGuide/Upgrade/UpgradePaths.htm?TocPath=Installing%20Vertica|Upgrading%20Vertica|_____1
You don't actually need to restart the database between each upgrade.
When you say user-defined functions, are these UDxs that you've built using R or Python? The backup should include them, but the code you'll need to store separately. The upgrade process won't remove them.

But that's a lot of upgrades. I'd definitely recommend a backup before you begin. Keep in mind that the recovery process is to delete everything and restoring to a clean 7,0 environment. I've never heard of anyone having to do that, though.

Thanks for the reply. Yes, user-defined functions are in Python.

You will need to recompile your UDx's for 9.3. See: https://www.vertica.com/docs/9.2.x/HTML/Content/Authoring/ExtendingVertica/UDx/UpdatingUDFLibraries.htm