* "Prefect" is a noun, meaning a student appointed to oversee other students, but it's not a verb. The sentence needs a verb to connect the subject "she" with the rest of the sentence.
* "After her offense" is a prepositional phrase modifying the verb, but we need the verb first.
Here are some possible corrections to make the sentence grammatically sound:
1. Using "is": "That she is still prefect after her offense" - This makes "is" the verb, connecting "she" to the state of being "prefect."
2. Using "remained": "That she remained prefect after her offense" - This uses the verb "remained" to show that her status as "prefect" continued despite the offense.
3. Adding "was": "That she was still prefect after her offense" - This uses the verb "was" to show that she was still a prefect, even after the offense.
The function of the corrected phrase would be a subordinate clause in a larger sentence. It functions as a noun clause, acting as the object of a verb like "said," "thought," or "wondered."
For example:
* "They wondered that she was still prefect after her offense."
* "It was shocking that she remained prefect after her offense."