# Suppose that the function T has period 7 and that T(0)=3

Suppose that the function T has period 7 and that T(0)=3.

Explain why T(-30)=T(40)?

Is it normal that teacher just tells you to read stuff in book and then do your homework, without explaining it? She was "teaching" some stupid stuff about graphing f(x)=(x-1)^2 + 2, which they teach you in Alg I and then gives you questions about periodic equations. Last two days one girl and me were the only ones to be able to do the homework. LeonhardEuler
Gold Member
If a function has a period, that means it repeats. Since the period is seven, that means that T(0)=T(7)=T(14)=... and that T(1)=T(8)=T(15)=.... In general it means that whatever value the function has at "a", it will have the same value at "a+7", "a+14", and so on. Do you see the solution now?

Doc Al
Mentor
What's the meaning of period? If the period is 7 (as given), what can you say about T(x) compared to T(x +7)?

I understand that every 7 the function repeats. But if I go 7 in positive and 7 in negative direction then I should have T(40)=T(-40) or T(30)=T(-30). Or am I missing something?

O damn. I got it. My bad. Thanks for help.

Doc Al
Mentor
You're missing something. Complete this list:
T(-30) = T(-30 + 7) [which is T(-23)] = T(-23 +7) ... and so on...

Shame on me. I calculated that there are 50 numbers between -30 and 40. I guess I'm to pised off.

HallsofIvy