scope of connection id (handler)

I've completed pseudo code for php script.

Simply, the initial script is called when the user completes specified
tasks, in this case a conditional group of up to 14. The script
interprets requirements and calls the appropriate scoring function.

Each function accesses a table, massages data, and writes the results
into another table. Straightforward stuff.

My question .... pg_connect is established in the main script. Does a
new connect have to made within each function? That's what I was doing
to prove the program workings at the function level, but now it is time
to tie it all together.

My confusion arises from the id being placed in $pg. How will/should/
must that be made available within the function so it can do its job?
Should it be passed? Declared as a global within the function? or must
I establish separate in-and-out-connections within each function?