Question

a periodic function, f, has a period of 12. if f(7)=-2 and f(11)=9 how would i determine the value of f(43), f(79), f(95), f(-1)

Answer 1

A period of 12 means the function keeps repeating the same values every 12 steps.
That means f(0)= f(12) , f(1)= f(13), or in general f(n)= f(n+12)

if you know f(7)= -2 then you know f(7+12) that is, f(19)= -2, and f(19+12) = f(31)= -2
and f(31+12)= f(43)= -2
Can you figure out the others?

Answer 2

so then i would do the same for f(79) right??
f(7+12) = f(19)
f(19 +12) = f(31)
f(31 +12) = f(43)
f(43+12) = f(55)
f(55+12)=f(67)
f(67+12)=f(79) ? -----> therefore f(79)=-2

what about for f(95) ?
... f(79 +12) = f(91)
f(91 +12 ) = f(103)


... :S im confused

Answer 3

Let's use a short cut. keep subtracting 12 from 95 until you get a small number.
7*12= 84 so if we subtract 12 from 95 7 times, we get to 95-84= 11
that means f(95) has the same value as f(11)

Answer 4

so when i subtract 12 for 95 i count how many times i do it until i get a low number?? :S

Answer 5

Not exactly. Here is what we are doing. We know f(7) and f(11).
We want to know what is f(95). To answer this, f(95) we have to figure out if f(95) is some multiple of 12 away from 7 or 11. We could just subtract 12 from 95, then subtract 12 again, and again. If we luck out, we will get either a 7 or an 11, and can answer the question.

Answer 6

But it is faster to say, "the biggest multiple of 12 I can subtract from 95 is 7*12 = 84"
95-84= 11
so we we know f(95)= f(11) and we know f(11)= 9, so f(95)= 9

Answer 7

so this applies with f(43) as well ? if we keep subtracting 12 to it we get either 7 or 11?

Answer 8

yes.

Answer 9

Or, if we get, for example 8, then we can't answer the question.

Answer 10

okay. i sort of get it. :S

Answer 11

is there an equation that i could use to find for any value of f(x) ?

Answer 12

First, can you answer f(-1)

Answer 13

f(-1) = 9
because f(-1+12) = f(11) ?

Answer 14

Yes.

The short way to do this is to use modulo arithmetic.

Have you studied this?
Given a number, example 43, find the remainder after dividing by 12:
43/12 = 3 remainder 7
so 43 mod 12 is 7

Answer 15

uh.. lol doesn't sound familiar..

Answer 16

Say we were given all 12 values, for
f(0), f(1), f(2), ... , f(11)
that means we can find any other f(n)
for example, f(14) 14/12 = 1 remainder 2
f(14) matches f(2), because 2 + 1*12 = 14

Answer 17

hmm. okay, thank you !