Answer
Yes.
Work Step by Step
Note that $f(0)=f(3)$, $f(1)=f(4)$, and $f(2)=f(5)$. Therefore, it can be speculated that $f(x)=f(x+3)$. Since there exists an $a$ such that $f(x)=f(x-a)$, this function is periodic with period of $3$.
Functions Modeling Change: A Preparation for Calculus, 5th Edition
by Connally, Eric; Hughes-Hallett, Deborah; Gleason, Andrew M.; Cheifetz, Phil C.
Published by
Wiley
ISBN 10:
1118583191
ISBN 13:
978-1-11858-319-7
Chapter 7 - Trigonometry and Periodic Functions - Review Exercises and Problems for Chapter Seven - Page 315: 7
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