<p>What is the best way to manage the JavaScript files and the functions/objects context in an ASP.NET MVC app?</p>

I put all my js files in the Content/Js folder. Then add URL helpers that allow me to change this in the future. My code isn't online, but I stole the idea from
Rob Conery MVC Commerce demo
.
Not sure what you mean by "manage...the functions/objects context in ASp.NET MVC app"
I think you're asking how to segment/partition your scripts. 
You should separate your JS files into separate chunks of functionality.