Implement the method by hand.

function map(arr, mapCallback) {
  // First, we check if the parameters passed are right.
  if (!Array.isArray(arr) || !arr.length || typeof mapCallback !== 'function') { 
    return [];
  } else {
    let result = [];
    // We're making a results array every time we call this function
    // because we don't want to mutate the original array.
    for (let i = 0, len = arr.length; i < len; i++) {
      result.push(mapCallback(arr[i], i, arr)); 
      // push the result of the mapCallback in the 'result' array
    return result; // return the result array

As the MDN description of the method.

The map() method creates a new array with the results of calling a provided function on every element in the calling array.