Has two related meanings: (1) 'through / by way of' a medium, means, or intermediary, and (2) 'throughout' an entire span of time or space. を通じて and を通して are largely interchangeable, though を通して slightly emphasizes active use of the means and を通じて is a touch more formal.
[Noun] + を通じて / [Noun] + を通して
友人を通じて彼女と知り合った。
Yuujin o tsuujite kanojo to shiriatta.
I got to know her through a friend.
友人 (friend) + を通じて marks the intermediary of the introduction.
この地方は一年を通して雨が多い。
Kono chihou wa ichinen o tooshite ame ga ooi.
This region has a lot of rain throughout the year.
一年 (a year) + を通して expresses the entire time span.
インターネットを通じて世界中の情報が手に入る。
Intaanetto o tsuujite sekaijuu no jouhou ga te ni hairu.
You can obtain information from all over the world via the internet.
インターネット + を通じて marks the means of access.
• Meaning 1: a medium/intermediary; Meaning 2: 'throughout' a whole period (一年を通して, 一生を通じて). • を通して slightly stresses actively going through the means; を通じて is a bit more formal. • Register: neutral to formal, common in writing.
The JLPT rarely asks whether you recognise a pattern — it asks which of several similar patterns fits. These are the ones を通じて/を通して is tested against.
によって marks the direct means/agent of an action, while を通じて/を通して implies passing through an intermediary or spanning a whole period.
にわたって stresses the extent/range something covers, whereas を通して as 'throughout' emphasizes continuity across the entire span.
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