<u>Answer</u>:
- The sign cautioned swimmers to stay within the designated swimming area–adverbial phrase.
- The lifeguards on the beach watched the swimmers carefully–adjectival phrase.
- Children and their parents built sandcastles with tall towers–adjectival phrase
- Seagulls soared over the water, searching for food–adjectival phrase.
<u>Explanation</u><em>:</em>
<em>- The sign cautioned swimmers to stay within the designated swimming area:</em>
In this sentence, the word "within" acts as an adverbial phrase telling us where the swimmers were asked to stay. And the words "stay within the designated swimming area" is a prepositional phrase since it uses the preposition "within".
<em>- The lifeguards on the beach watched the swimmers carefully</em>:
Remember, adjectives are known for ending with 'ly', and the word "carefully" modifies the sentence, telling us how the lifeguards watched the swimmers.
<em>- Children and their parents built sandcastles with tall towers:</em>
This is the case because the adjective "tall" is used in the sentence to modify the word "tower", in a sense telling us the type of towers built.
<em>- Seagulls soared over the water, searching for food:</em>
The adjective "searching" is used to modify the entire sentence telling us what the Seagulls soared the waters for.