Edit in JSFiddle

var f = function(arg) {
    if (arg != null) {
        document.write(arg);
        document.write("<br/>");
    } else if (arg == undefined) {
        document.write("undefined<br/>");
    }
    else {
        document.write("<br/>");
    }
};
// type testing functions - lets us find out the type
f($.isArray(["1", "2"]));
f($.isFunction(f));
f($.isEmptyObject({})); f($.isEmptyObject({name:"xyz"}));
f($.isPlainObject({name:"xyz"})); f($.isPlainObject("xyz"));
f($.isNumeric(5));
f($.isWindow(this.window));
f($.type(f)); f($.type(5)); f($.type([])); f($.type({})); f($.type("abc"));
f($.type(this.window)); f($.type(document)); f($.type(this));

//array manipulation
f('');
var arr1 = [1,2,3,4,5,5];
f($.inArray(4, arr1)); f($.inArray(99, arr1)); // search value in array. returns the position
f($.unique(arr1));
f($.merge(arr1, [5,6,7]));
//transform each item into something else
f($.map(arr1,function(item, idx){
    return item + "a";
}));
//select only those items which match a criteria
f($.grep(arr1, function(item){
    return item <= 4;
}));
// convert array like object into javascript array
var arr2 = $.makeArray(10);
f($.merge(arr1, arr2));
// slice
var arr3 = [7,8,9,10];
f(arr3.slice());
f(arr3.slice(1));
f(arr3.slice(1,3));
f(arr3.slice(0));