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Thread: Graphing using largest integer function

  1. #1
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    Graphing using largest integer function

    The question is:
    "The symbol [x] denotes the largest integer which is less than or equal to x. For example [2.4] = 2, [3] = 3, [-1.2] = -2. Draw the graph of: (see attached)

    Any help would be greatly appreciated, I am really stumped as to how it would look.
    Attached Thumbnails Attached Thumbnails Graphing using largest integer function-img_0335.jpg  
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  2. #2
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    Re: Graphing using largest integer function

    on the interval $[0,1)$, $y_0 = 0 + \sqrt{x - 0} = \sqrt{x}$

    on the interval $[1,2)$, $y_1 = 1 + \sqrt{x - 1}$, the graph of $y_0$ shifted right one unit and up one unit

    on the interval $[2,3)$, $y = 2 + \sqrt{x - 2} = 1 + \left[1 + \sqrt{(x-1)-1}\right]$, the graph of $y_1$ shifted right one unit and up one unit

    the pattern repeats on subsequent (and prior) intervals ...
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    Re: Graphing using largest integer function

    Quote Originally Posted by thebestrose828 View Post
    The question is:
    "The symbol [x] denotes the largest integer which is less than or equal to x. For example [2.4] = 2, [3] = 3, [-1.2] = -2. Draw the graph of: (see attached)
    Any help would be greatly appreciated, I am really stumped as to how it would look.
    Here is the plot.
    In most cases, in modern mathematics the floor function is substituted for the greatest integer fumction.
    Last edited by Plato; Apr 16th 2017 at 11:55 AM.
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