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Math Help - newbie needing analytical description of a periodic function

  1. #1
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    newbie needing analytical description of a periodic function

    I have this function here.

    newbie needing analytical description of a periodic function-untitled-1.jpg

    Can someone please explain why from 4 < x < 10 it is 7 - x?
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Well, two points make a line. Take the two endpoints and see what you get.
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  3. #3
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    not really sure. From 0 < x < 4 its 3x/4 but cant see why its 7 - x.
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  4. #4
    MHF Contributor chisigma's Avatar
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    You have a function...

    f(x)= a_{0} + a_{1}\ x (1)

    ... and is f(4)=3 and f(10)=-3... then You can find a_{0} and a_{1} in 'standard way'...

    Kind regards

    \chi \sigma
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  5. #5
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    rossy54, the function changes from place to place. From 0 to 4 it is indeed 3x/4. However, it immediately changes to 7-x when x is between 4 and 10. After that it is a constant.
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  6. #6
    Senior Member yeKciM's Avatar
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    to make equation of line through two points :

     (y-y_1)=\displasyle \frac{y_2-y_1}{x_2-x_1} \cdot (x-x_1)

    now your two points  M_1 (4,3) \; M_2(10,-3)

    so you will have

    \displaystyle  (y-3)=\frac{-3-3}{10-4} \cdot ( x-10)

    \displaystyle  (y-3)=\frac{-6}{6} \cdot ( x-10)

    \displaystyle  y-3= 10-x

    \displaystyle  y=7- x


    if you don't trust me just put any x from 4 to 10 and you will get exact value of y...
    for example x=7 -> y=0 (as you see on graphic)



    if u need to represent your function over step functions it would be like this

     x(t) = \frac{3t}{4}[u(t)-u(t-4)] + (7-t)[u(t-4) - u(t-10)]


    P.S. you can take any two points from that line and put in formula and you will get same result (doesn't have to be "start" and "end")
    Last edited by yeKciM; August 14th 2010 at 04:56 PM.
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