Arabic to Greek numeral converter, 1 - 10
Reviewing your current structure: your return ""; could be improved: it should / could be inside the switch statement as a default case.



It's better to use an object here, as later you can extend it without having to spend pointless LoCs on cases and breaking.

function arabicToGreek(input) {
    'use strict';
    var greek = {
        1: "α",
        2: "β",
        3: "γ",
        4: "δ",
        5: "ε",
        6: "ϝ",
        7: "ζ",
        8: "η",
        9: "θ",
        10: "ι"
    };
    //
}


Then, add greek.hasOwnProperty to check that your string is a valid object property, in which case that it isn't, you can throw an error.

if (!greek.hasOwnProperty(input)){
    throw new Error("input not a valid integer representing a character");
}


This also means you can store the greek characters and potentially other languages in an external JSON document.