Here's why:
* Prepositional phrases start with a preposition (like *at*, *on*, *in*, *with*, *by*, etc.) and are followed by a noun or pronoun called the object of the preposition. For example: "at the store," "on the table," "in the car," "with a smile," "by the river."
* Adverbial phrases modify verbs, adjectives, or other adverbs, providing information about time, place, manner, or degree. In the case of "at first," it tells us about the time when something happened.
Example:
> "At first, I was nervous, but then I relaxed."
In this sentence, "at first" modifies the verb "was." It tells us when the speaker felt nervous.