I just got into a discussion with a friend who said that in Islam, we do not believe that death is preordained. The time of death is not fixed and depends on the choices we make. Furthermore he added that prayers (Du'a) can increase or decrease persons lifespan, that is if you ask for a longer life God will grant it and if you ask for a quick death God will grant that too.From what I know time of death is fixed at birth and no amount of action or Du'a can change that.I would be extremely grateful if you can send me Qur'anic verses or Hadith that support either views, so that this confusion is cleared.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Allah has predetermined a fixed life period of everyone; when that fixed time comes, his life comes to an end.
Allah Says (interpretation of meaning): {… when their term is reached, neither can they delay it nor can they advance it an hour (or a moment).} [7: 34].
A person does not have any choice in this matter. Even though making Du'a for a long life or a short life is allowed provided the intention behind the Du'a for long life is to do more good deeds and the intention behind Du'a for a short life should be to avoid trials. It is reported in a Hadith that Allah Said to the Prophet (Sallallahu Alaihi wa Sallam): "When you perform a prayer say: 'O Allah! I beg you to make me do good deeds, and abandon abominable deeds, and to love the poor and the needy, and when you intend to put people to trial cause me to die unblemished" [ al-Tirmizi , Sheikh al-Albani considered it Sahih].
The increase or decrease that occur in the duration of lives through Du'a is not contrary to what Allah has predetermined, i.e. the fixed durations of lives. The changes do not happen in the knowledge of Allah or in al-Lauh al-Mahfooz (the preserved Tablet) rather they occur in the knowledge of the angel who is authorized to take the souls of people.
For example, Allah predetermines of duration one's life as sixty years if he keeps good kinship with his relatives; otherwise, his age is forty years. Allah knows what the person will do whether he will maintain kin relations or cut them off. Allah's knowledge does not change as proved in many verses. But what is in the knowledge of the angel is subject to changes based on the changes in the condition of the person from good to bad or vice versa. This point is stated in the verses: {Allâh blots out what He wills and confirms (what He wills). …} [13: 39].
The above clarification removes the doubts in the given matter.
Allah knows best.