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Looking at the function, the pattern seems to repeat itself on both sides, which would make it a periodic function.
It's hard to tell based on the domain of the plot you're given. For all we know, for \(x\ge6\) the function could be veering off to infinity. So technically, although it looks like it's periodic, we can't say for sure based on just this info. Do you have the actual function, or were you just given the plot?
We were just given the plot @sithsandgiggles
Then I guess you can assume it's periodic. This is for a pre-calc/calc-level course, right?