Need 1. which sentence uses an infinitive as an adverb? a) my favorite board game to play is stored in the basement. b) nicole wants to learn the art of rhetoric before next year. c) dave's favorite thing to do is to walk his dog every evening. d) we met after school to study for the big math test next week. 2) which sentence includes an infinitive used as a direct object? a) as a new faculty member, susan wanted to succeed. b) to win requires an enormous effort from our team. c) golnesa’s career goal, to write, was never quite met. d) the principal of the school is the individual to notify. 3) which sentence uses an infinitive as an adjective? a) to become an engineer has always been a dream of mine. b) sally tried to play the guitar, but she became a singer instead. c) fred was a serious soccer player and was determined to win each game. d) the best way to learn to make biscuits is to talk to my mom. 4) identify the gerund phrase, the direct object of the verb requires. a) the job requires getting your hair cut to a short, safe length. b) the job requires getting your hair cut to a short, safe length. c) the job requires getting your hair cut to a short, safe length. d) the job requires getting your hair cut to a short, safe length.

1. The correct answer is D)We met after school to study for the big math test next week. 
The infinitive here is the phrase 'to study,' and it functions as an adverb in this sentence. You can easily determine that by asking the adverbial question 'Why?' Why did we meet? - To study for the big math test next week. That way you know it's an adverb.

2. The correct answer is A)As a new faculty member, Susan wanted to succeed.
Here, the infinitive is 'to succeed,' and it functions as the direct object of the sentence. You can simply ask the question 'What?' in order to determine a direct object. What did she want? To succeed. That way you know it's a direct object.

3. The correct answer is D)The best way to learn to make biscuits is to talk to my mom. 
There are two infinitives in this sentence, to learn and to make. However, the latter is used as a direct object, whereas the former functions as an adjective. Adjectives are found near nouns and describe them in more detail - here, the infinitive 'to learn' describes the noun 'way.'

4. The correct answer is The job requires getting your hair cut to a short, safe length.
You've written the same example for all options, however, it is the correct answer nevertheless. The gerund here is 'getting,' and it functions as the direct object of the verb 'requires.' What does the job require? Getting your hair cut.