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Math Help - graph mod

  1. #1
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    graph mod

    y=mod(x-2)+mod(x-3)+mod(x-4) in this i have found following cases

    x<2 x belongs to (2,3) x belongs to (3,4) x>4

    can yu please suggest the graph of the equation above
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  2. #2
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    I would suggest graphing \displaystyle |x - 2|, |x - 3| and \displaystyle |x - 4|, then using addition of ordinates to graph \displaystyle |x - 2|+|x-3|+|x-4|.
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  3. #3
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    You are correct in identifying the intervals where the function behaves differently. Consider each interval in turn. For example, if x < 2, then x - 2 < 0, x - 3 < 0 and x - 4 < 0. For all a < 0, mod(a) = -a. (They usually write abs(a) for the "absolute value.") So, mod(x-2)+mod(x-3)+mod(x-4) = -(x - 2) - (x - 3) - (x - 4) = -x + 2 - x + 3 - x + 4 = -3x + 9. If 2 <= x < 3, then x - 2 >= 0, x - 3 < 0 and x - 4 < 0. Therefore, mod(x-2)+mod(x-3)+mod(x-4) = x - 2 - (x - 3) - (x - 4) = x - 2 - x + 3 - x + 4 = -x + 5. You have to do similar calculations for the remaining two intervals.
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    can yu please show the graph
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  5. #5
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    To draw a graph of y = -3x + 9 on the interval x < 2, you need to find two points and draw a line through them. For example, y = 9 for x = 0 and y = 0 for x = 3. You only need a part of that line that is located above the interval in question (marked in bold). Do a similar thing for the other three intervals.
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    Quote Originally Posted by emakarov View Post


    To draw a graph of y = -3x + 9 on the interval x < 2, you need to find two points and draw a line through them. For example, y = 9 for x = 0 and y = 0 for x = 3. You only need a part of that line that is located above the interval in question (marked in bold). Do a similar thing for the other three intervals.

    thanks
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