Answer
No.
Work Step by Step
If this function is pushed rightward, it will always create a new function. Therefore, there's no real number $a$ such that $f(x)=f(x-a)$. This function is not periodic.
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: 6
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