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    Without drawing a sketch, how would you find out if this is even or odd? I mean without the sketch, via calculations, f(2pi) = f(-2pi) suggesting that it is an even function.. But that isn't the case?
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    The function f(x)=x2 is even for all values of x because (-x)2 = x2, so f(t) is even



    The graph is misleading as it is not t2
    according to the graph:
    f(1) \neq f(-1) therefore function is not even
    f(1) \neq -f(-1) therefore function is not odd
    therefore function is not even or odd
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    If you restrict the domain to 0 \le t \le 2\pi, then y=t^2 is neither odd nor even as it's not even defined for -ve t.

    However, you can create a periodic function on \mathbb{R}, by repeating the graph you have on the restricted domain, either via an odd extension or an even extension. In the picture you gave, the function has an neither an even nor odd extension since neither f(-t)=f(t) nor f(-t)=-f(t) are true.

    I guess this is something to do with Fourier series?
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    (Original post by atsruser)
    If you restrict the domain to 0 \le t \le 2\pi, then y=t^2 is neither odd nor even as it's not even defined for -ve t.

    However, you can create a periodic function on \mathbb{R}, by repeating the graph you have on the restricted domain, either via an odd extension or an even extension. In the picture you gave, the function has an neither an even nor odd extension since neither f(-t)=f(t) nor f(-t)=-f(t) are true.

    I guess this is something to do with Fourier series?
    Yes this is from a lecture on Fourier series. One thing I am confused about: if I was told to sketch f(t) = t^2, and 0<t≤2pi and I sketched the following (without repetition) would I still yield the correct answer if I deduced whether it is even or odd based on this non-repeated form?
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    (Original post by GPODT)
    Yes this is from a lecture on Fourier series. One thing I am confused about: if I was told to sketch f(t) = t^2, and 0<t≤2pi and I sketched the following (without repetition) would I still yield the correct answer if I deduced whether it is even or odd based on this non-repeated form?
    The question "is this function odd or even?" is not meaningful: a function which is not defined for negative values cannot be even or odd. There is no "deduce whether a function is even or odd from its restriction to [0, 2\pi]".
 
 
 
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