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Thread: graph of a function

  1. #1
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    graph of a function

    i have a periodic function f(t) = f(t + 2pi)

    it is valid over the intervals:

    0 ( -pi < t < 0)
    t (0 < t < pi)

    I need to sketch the graph over three periods.

    Will it be continuous like a curve or is it a straight line for the interval 0 and a curve for interval t?

    cheers
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by iwishiunderstood View Post
    i have a periodic function f(t) = f(t + 2pi)

    it is valid over the intervals:

    0 ( -pi < t < 0)
    t (0 < t < pi)

    I need to sketch the graph over three periods.

    Will it be continuous like a curve or is it a straight line for the interval 0 and a curve for interval t?

    cheers
    what do you mean by that?

    $\displaystyle f(t) = \left\{ \begin{array}{rl} 0, &-\pi < t \leq 0 \\ t, & 0 < t \leq \pi \end{array}\right.$
    is this?
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by iwishiunderstood View Post
    i have a periodic function f(t) = f(t + 2pi)

    it is valid over the intervals:

    0 ( -pi < t < 0)
    t (0 < t < pi)

    I need to sketch the graph over three periods.

    Will it be continuous like a curve or is it a straight line for the interval 0 and a curve for interval t?

    cheers
    It will not be continuous because $\displaystyle \lim_{t \to \pi ^-}f(t) \neq \lim_{t \to \pi ^+}f(t)$.

    This will be something like a sawtooth function: It will be a horizontal line (on the t axis), then a straight line at a 45 degree angle from 0 up to $\displaystyle \pi$, then back down to zero again.

    -Dan
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  4. #4
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    thanks for the help. Just to clarify - the second line will come up to pi on vertical axis then it will drop to 2pi on the horizontal axis (in other words it will drop down to zero after 1 period)????


    cheers again.
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