Berikut adalah penjelasan mengenai fungsi Noun Clauses yang diawali dengan "that" dalam kalimat-kalimat tersebut:

a. They were afraid that the lion would eat them.

  Fungsi: Object of preposition ("that the lion would eat them" berfungsi sebagai objek dari preposisi "that").

b. That she wouldn't forgive me made me upset.

  Fungsi: Subject ("That she wouldn't forgive me" berfungsi sebagai subjek dari kalimat tersebut).

c. The up-to-date information about Coronavirus is that the number of victims is increasing day by day.

  Fungsi: Subject complement ("that the number of victims is increasing day by day" berfungsi sebagai pelengkap subjek dari kalimat tersebut).

d. She knows in that the tuition will rise in the next academic year.

  Fungsi: Tidak ada fungsi yang tepat dalam kalimat ini. Struktur kalimatnya tidak gramatikal.

e. The government announced that this month the vaccine would be given for free to all citizens.

  Fungsi: Object ("that this month the vaccine would be given for free to all citizens" berfungsi sebagai objek dari kata kerja "announced").

Jadi, dalam kalimat-kalimat tersebut, fungsi noun clauses yang diawali dengan "that" dapat berperan sebagai object of preposition, subject, subject complement, atau object.