Since the model component of MVC handles the inserts, updates, and deletes should I create one class for the database connection. Which design pattern would this fall under?
There is no single design pattern for this. Data Access Objects are quite common, though.
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus
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a bit of art, as a gift, the permaculture playing cards