1 MySql connection vs. er, more then 1

Hi guys

Very quick question, I’m just wondering which is more resourceful for connecting to a MySql db from PHP - having just one connection that persists throughout the site, or creating a connection everytime a query is run…

For example, say that I create a function that runs mysql_connect() and mysql_select_db(), and call this function everytime I run a query, is this just a horrible use of resources, and is it more beneficial to just run these once within a function file that gets included in each page?

Thanks guys, hopefully I’ve made myself clear, and I probably know the answer already, just want to make sure!!!