Take another look at the passage:
Farah woke Kirby, the family's ancient German shepherd. To see if he had fallen asleep on the remote control. The growl that Kirby rumbled in protest convinced Farah to use the channel buttons on the front of the television instead.
You chose the third part, The growl that Kirby rumbled in protest convinced Farah .... This part has a main clause: growl is the subject; convinced is the verb. A fragment will not have a main clause.