## Adorkable Group Title Periodic Functuions. A periodic Function f(x) has a period of 12. If f(7)=-2 and f(11)=9, determine the value of f(43). Please explain thoroughly. one year ago one year ago

1. hartnn Group Title

since the function is periodic with period 12, f(43) = f(43-12) = f(31), did u get this ?

I think so. So if for example in the same context if the question was f(79) then it would be f(79 - 12) = f(67) ?

3. hartnn Group Title

yes.

4. hartnn Group Title

f(31) = f(31-12) = f(31-12-12) and so on...

Woah. Why would you subtract 12 twice or more times? And what do we figure out when we do that?

6. hartnn Group Title

because for every interval of 12, the function has same value.... so if i add or subtract 12, the value of function is same $$f(x\pm 12 )= f(x)$$

7. hartnn Group Title

more specifically $$f(x\pm n*12 )= f(x)$$

8. hartnn Group Title

n can be any natural number .

9. hartnn Group Title

so, f(43) = f(43-12) = f(31) = f(31-12) =.... do this till u get something you know the value of.

not quite sure im understanding.

11. hartnn Group Title

f(43) = f(31) u got this ?

12. hartnn Group Title

no?

13. hartnn Group Title

well, i'll write out steps, see if u get it $$f(43)=f(43-12)=f(31)=f(31-12)=f(19)=f(19-12)=f(7)=-2$$

Okay I got everything except the f(7)

Because 19-12 equals 7 but, then 7-12 is equal to -5

16. hartnn Group Title

but u already have f(7) = -2 so u get f(43) = -2

17. hartnn Group Title

and yes, f(-5) also equals -2

sotheanswer coulve been -5 or -2?

19. hartnn Group Title

no, not -5 . f(43) = f(7) = -2

hmm. Can we try another example please? say f(-1)?

21. hartnn Group Title

for the same periodic function ?

yes

23. hartnn Group Title

ok, f(-1) = f(-1+12) = ?

11

So it can be plus or minus?

26. hartnn Group Title

its f(11) yes, + or -12 ...

27. hartnn Group Title

f(-1) = f(11) = 9

Okay. I have an idea of what youre talking about. I'll try this one and can you see if it is correct for me? Same function.

f(95)

30. hartnn Group Title

yes, try it ..

Would it be f(95)=f(11)=9 so far am i correct?

32. hartnn Group Title

yes, ver correct :)

Okay! Thank you once again so much for your patience and time!! Im going to best response all your answers!