I'd personally reccomend PHP Objects, Patterns and Practice
Disk is a slowest part of the server, so in this case variant "all functions in 1 file" will give you little more performance, theoretically.
But I don't recommend you to create "functions.php", better way is OOP. Create classes (objects) with methods, use autoloaders and PSR-0 standard and you will forget about "include" and "require" at all.
Good book about patterns and design