Learn Farsi: آن‌ها در یک جزیره‌ی ناشناخته زندگی می‌کنند.

It uses the negative prefix nâ-, which flips the meaning of the word it attaches to. Here, it is added to shenâkhte (known or recognized) to mean unknown.

What type of word is shenâkhte before the nâ- is added?

It is a past participle. It comes from the verb shenâkhtan (to know or recognize). In Farsi, you can frequently create negative adjectives by attaching nâ- directly to a past participle.

Why is there an extra ی at the end of jazire (island)?

This is the ezâfe, the grammatical link connecting a noun to its adjective. Because jazire ends in a silent 'e' (written with the letter ه), the ezâfe requires a 'y' sound to bridge the vowels smoothly. This is written as ی, making the pronunciation jazire-ye nâshenâkhte.

Why does the Farsi sentence use dar (in) when the English translation says "on" an island?

Prepositions rarely map perfectly between languages. While English treats an island as a surface you live "on", Farsi treats it as an enclosed geographic area or territory that you live "in" (dar).