zutun
to close
To close something, for example a door, a window, or your eyes. It is a synonym of 'zumachen' (to close).
Tu bitte die Tür zu, es ist kalt draußen.
Please close the door; it's cold outside.

to close / add
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to close
To close something, for example a door, a window, or your eyes. It is a synonym of 'zumachen' (to close).
Tu bitte die Tür zu, es ist kalt draußen.
Please close the door; it's cold outside.

'Zutun' (to close / add) is a separable verb with the prefix 'zu'. In a main clause, 'zu' comes at the end. In subordinate clauses and in the infinitive, the verb stays together.
Kannst du bitte das Fenster zutun?
Can you please close the window?
You can recognize the meaning from the object: If it is about things that can be opened and closed, e.g. 'Tür' (door), 'Fenster' (window), or 'Augen' (eyes), 'zutun' means to close. In the context of cooking or mixing, it means 'hinzufügen' (to add).
Er tat die Augen zu und schlief sofort ein.
He closed his eyes and fell asleep immediately.
A very common fixed expression is 'kein Auge zutun'. It means that someone cannot sleep at all the whole night.
Wegen des Lärms konnte ich die ganze Nacht kein Auge zutun.
Because of the noise, I couldn't get a wink of sleep all night.
In the meaning 'schließen' (to close), 'zutun' is used mainly in spoken, informal language. It often sounds more personal or everyday.
Tu mal schnell die Jacke zu, es wird kühl.
Quick, zip up your jacket; it's getting chilly.
to open
'öffnen' and 'zutun' are opposites when talking about things like doors, windows, or eyes. 'öffnen' means that something is opened and becomes accessible. 'zutun' means that you close something; it is close to 'zumachen' and sounds more colloquial. In more formal situations, 'schließen' is often more natural than 'zutun'. In everyday speech, however, you can easily say: 'Mach bitte das Fenster zu' (Please close the window) or 'Tu bitte das Fenster zu' (Please close the window).

Die Kundin tut die Tasche zu, bevor sie den Laden verlässt.
The customer closes her bag before leaving the store.
Wir öffnen morgens die Fenster, damit frische Luft ins Zimmer kommt.
We open the windows in the morning so that fresh air comes into the room.