He must like studying calculus.

Whats the noun function?

What is the gerund phrase?

He must like

Nope.

"Recognize a gerund phrase when you see one.
A gerund phrase will begin with a gerund, an ing word, and will include other modifiers and/or objects. "


http://www.chompchomp.com/terms/gerundphrase.htm

Do you understand what Ms. Sue posted for you? Especially this??

... an ing word ...

??

The noun function in this sentence is "studying." It is the gerund form of the verb "study," and it is acting as a noun in the sentence. It serves as the subject of the sentence and describes an action or activity that the person enjoys or is involved in – in this case, studying calculus. To identify the noun function in a sentence, it is helpful to look for words that are acting as subjects, objects, complements, or modifiers within the sentence structure.