It doesn't matter what file the JavaScript function came from as long as it was parsed and executed. You can check whether it's available as a function in the global scope by typing the following in your console:
console.log( function_tester );
or
console.log( window.function_tester );
If that fails either your function hasn't been defined or hasn't been defined in the global scope (hence why it isn't a member of the global window object).
Any chance the function is not just inside an external file, but also not in the top-level inside that file, for example, inside another function. Like so:
On a totally separate note, no need for the .each above. The .slider call will automatically do the .each iteration internally on all matched elements from your selector, and it initializes them each as separate slider widgets.