Syntactic functions of the Participle in the sentence?

Participle can be used as an attribute; adverbial modifier of time, cause, manner; predicative.

The fence surrounding the garden is newly painted. (attribute)

Having reached the classroom, she became the object of many questions. ( adverbial modifier of time)

Having been a little in that line myself, I understood it. (cause)

Gwendolen was silent, again looking at her hands. (manner)

The effect of her Words was terrifying. (predicative)