Various implementations of `map` using recursion.

recursive.js

function first(xs) {
    return xs[0];
};

function rest(xs) {
    if (xs.length <= 0) {
        return [];
    }
    return xs.slice(1, xs.length);
};

function conj(xs, x) {
    var t = xs;
    t.push(x);
    return t;
};

function cons(x, xs) {
    var t = xs;
    t.unshift(x);
    return t;
}

function map(xs, f) {
    if (xs.length <= 0) {
        return [];
    }
    return cons(f(first(xs)), map(rest(xs), f));
};

// OR:

function map_ternary(xs, f) {
    return xs.length <= 0 ? [] : cons(f(first(xs)), map_ternary(rest(xs), f));
}

// NOTE: This doesn't work in JS no TCO -- see https://en.wikipedia.org/wiki/Tail_call
function map_iter(xs, f) {
    function iter(xs, f, acc) {
        if (xs.length <= 0) {
            return [];
        }
        return iter(rest(xs), f, conj(acc, f(first(xs))));
    };
    return iter(xs, f, []);
}

function inc(x) { return x + 1; };

map([1,2,3,4], inc);
map_iter([1,2,3,4], inc);
map_ternary([1,2,3,4], inc);