Final answer:
The phrase 'to understand her math better' in the sentence is an adverb phrase, as it modifies the verb 'signed up' and provides more information about Delilah's reason for taking the extra class.
Step-by-step explanation:
In the sentence, 'To understand her math better, Delilah signed up for an extra class,' the phrase 'to understand her math better' is an adverb phrase.
Adverb phrases modify verbs, adjectives, or other adverbs and answer questions like 'how,' 'when,' 'where,' 'why,' or 'to what extent.'
In this sentence, the adverb phrase 'to understand her math better' modifies the verb 'signed up,' giving us more information about Delilah's reason or purpose for signing up for an extra class.