If you update the theme periodically then yes the changes would get overwritten..
An easy solution would be to keep your own generic plugin, and add functions directly into that file instead (it'll work just aswell there as in the theme's functions.php)..
This is all the code required to create a plugin file..
Plugin Name: A Name For Your Plugin
NOTE: There are of course various other pieces of information you can include in the top of the plugin file, but really for personal plugins(with your own code), only the name is required(to make it work - and be able to identify it's yours).
As many or as few functions as you like can sit below that code.. so just go ahead and add the above, plus any functions from the tutorials into the file and save it with a php extension. Upload the file to your plugins folder, and activate it like you would any plugin..
Once it's active, modify/update the file as often as you like...
The code will operate perfectly fine this way, and you'll not lose changes to the code, since it will exist independantly from the theme..