Answer:
The house was shut down for the night, having read the children a bedtime story.
Explanation:
A modifier gives more reason or undertone about a sentence. So by using the sentence as it's given in the sentence; it doesn't show it's function but in the rewritten form it does just that. It explains why the door was shut down for the night.
The first sentence, ‘My cat’s favorite pastime seems to be sleeping’.
A gerund is when a vets is used as a noun.
Future tip: gerunds most always end in ‘ing’.
Hope this helps.