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A quick run here. This is not foolproof though. I might be missing many things here. You can invest more time and improvise this. But this might give you the basic idea. Anyways its always better to use the native functions as they are much more optimised and cover many edge cases.

JSFiddle link https://jsfiddle.net/theevilhead/cpnsbwt4/

const values = [2, 3, 4, 7, 41, 22];

// Custom map
Array.prototype.customMap = function(callback) {
    const mappedArray = [];
    for (var i = (this.length - 1); i >= 0; i--) {
              mappedArray.unshift(callback(this[i], i));
         }
  return mappedArray;
}

const ma = values.customMap((val, index) => 2 * val)
console.log("Map", ma)

// Custom filter
Array.prototype.customFilter = function(callback) {
  const filteredArray = [];
  for (var i = (this.length - 1); i >= 0; i--) {
    callback(this[i]) && filteredArray.push(this[i])
  }
  return filteredArray
}

const fa = values.customFilter(val => { return (val > 5) })
console.log("Filter", fa)

// Custom reduce
Array.prototype.customReduce = function( callback ) {
  let acc = 0;
  const arrLength = this.length;
  for (var i = 0; i < arrLength; i++) {
    acc = callback(acc, this[i], i, this);
  }
  return acc;
}

const ra = values.customReduce((acc, curVal, curInd, srcArr) => {
  return acc + curVal
});
console.log("Reduce", ra)