Everything in JS is bound to containing scope. Therefore, if you define a function directly in file, it will be bound to window object, i.e. it will be global.

To make it "private", you have to create an object, which will contain these functions. You are correct that littering global scope is bad, but you have to put something in global scope to be able to access it, JS libraries do the same and there is no other workaround. But think about what you put in global scope, a single object should be more than enough for your "library".

Example:

MyObject = {
    abc: function(...) {...},
    pqr: function(...) {...}
    // other functions...
}

To call abc for somewhere, be it same file or another file:

MyObject.abc(...);

yes it's valid.

if you don't want to pollute the global scope (and to avoid clash by name) a best practise is to wrap your functions inside an object and expose the object to the global scope

this is an example, but the idea is to bundle together the functions base on their behaviour

<script type="text/javascript">
  (function(global){

    function setCookie(cname,cvalue,exdays) {
        var d = new Date();
        d.setTime(d.getTime() + (exdays*24*60*60*1000));
        var expires = "expires=" + d.toGMTString();
        document.cookie = cname + "=" + cvalue + ";" + expires + ";path=/";
    }

    function getCookie(name) {
        var value = "; " + document.cookie;
        var parts = value.split("; " + name + "=");
        if (parts.length == 2) return parts.pop().split(";").shift();
    }

    global.bundleObj = {
      setCookie: setCookie,
      getCookie: getCookie
    }

  })(window)
</script>

then anywhere in your code

<script>
  window.bundleObj.setItem()
</script>