The function f is periodic. If f(3) = -3, f(5) = 0, f(7) = 3, and the period of the function of f is 6, then how do you find f(135)?

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Answer 1 · 2015-12-09T10:40:05

#f(135)=f(3)=-3#

If the period is #6#, it means that the function repeats its values every #6# units.

So, #f(135)=f(135-6)#, because these two values differ for a period. By doing so, you can go back until you find a known value.

So, for example, #120# is #20# periods, and so by cycling #20# times backwards we have that

#f(135)=f(135-120)=f(15)#

Go back a couple of periods again (which means #12# units) to have

#f(15)=f(15-12)=f(3)#, which is the known value #-3#

In fact, going all the way up, you have

#f(3)=-3# as a known value

#f(3)=f(3+6)# because #6# is the period.

Iterating this last point, you have that

#f(3)=f(3+6)=f(3+6+6)=f(3+6+6+6)=...=f(3+132)=f(135)#, since #132=6*22#