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If F is any function with a period of $6$, determine the period of each related function below:

$y = f(x+1)$

$\displaystyle y = f(\frac{x}{2})$

I know that the basic definition of a period is $f(x) = F(x + P$), but I don't really understand what this question is asking. Do we substitute $6$ for $y$ and solve?

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the first change shifts the whole function by 1 to the left - does this change the period?

The second function rescales the argument in such a way that what took $d$ before now takes $2d$. Does this change the period, and if so, how?

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Ok, I see it now. So the first one would have the same period, but for the second one, you would divide the period by 1/2 (multiply by two), so the period for the second one would be 12. Thanks! – kindalost Feb 28 '13 at 20:54

Clearly, y=f(x+1)just shifts the original one to the left by 1, so the period remains;
for y=f($x\over2$), it enlarge the function twice in the direction of x-axes so the period is 12.

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