How is the phrase "swimming laps" functioning in the following sentence? my grandmother's favorite form of exercise is swimming laps. a. it's the subject of the sentence. b. it's the direct object. c. it's a subject complement. d. it's the object of a preposition.

The phrase swimming laps is used as C. subject complement of this sentence.
Since it is preceded by a linking verb is, it cannot be a direct object. And since the phrase my grandmother's favorite form of exercise is subject, it cannot be the subject either. There is no preposition before it, so it is not the object of a preposition. 

I’d go with letter d