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Greatest integer function: Textbook wholly inadequate

  1. Oct 27, 2005 #1
    This should be a simple question to answer… I’m doing a high school correspondence course, Algebra 2 and I’m trying to understand the “greatest integer function” which apparently has something to do with Step Functions…
    They give me very little to go one, a few tables and graphs which don’t mean anything to me.
    The problem I’m trying to solve is this:
    Evaluate f(3/4) if f(x)=[[1-2x]]
    The double brackets are basically what the symbol looks like in my book.
    So how do I “Evaluate” it? What in the world do I evaluate? The examples they give me are not in the above questions format, so I can’t draw any parallels to understand what they are doing!
    They give me some answers to choose from (multiple choice) and they are just numbers between -2 and 1.
    Any help would be appreciated, like maybe a link somewhere I could get a descent explanation of solving problems like the one above.
    Here are some screen shots of the two pages in my textbook that talk about step functions, which I have yet to understand how their examples could possibly help answering the problem they gave me.
    Thanks,
    Alan
    [​IMG]
    [​IMG]
     
  2. jcsd
  3. Oct 27, 2005 #2
    All you need to know is what they wrote in italics: "The symbol [[x]] means the greatest integer less than or equal to x." The rest shows that f(x)=[[x]] is one example of a step function.
     
  4. Oct 27, 2005 #3
    Unfortunately I do need to know more than that! :cry:
     
  5. Oct 27, 2005 #4

    shmoe

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    To find [[x]], put x on the number line. Start moving to the left, the first integer you hit is [[x]]. If x is already an integer then you'll have [[x]]=x

    For example, if you start at 2.495 and go left, the first integer is 2, so [[2.495]]=2. If you start at -0.6, the first integer as you go left is -1, so [[-0.6]]=-1.

    If you're already on an integer, you don't go anywhere, so [[2]]=2, [[5]]=5, [[-123]]=-123.

    Can you find [[4.6]], [[4.99]], [[16.0]], [[-6]], [[0]], [[-4.6]] now?

    Why this is called the "Greatest Integer Function"- if you look at all the integers less than or equal to x, then [[x]] is the largest among them. If x=2.495, the integers less than x are 2, 1, 0, -1, -2, -3, .... and so on. The largest of these is 2, which is what we said [[2.495]] was.

    Now your f(x)=[[1-2x]] is dealt with like any other function. To find f(3/4) substitute 3/4 for x and go from there.
     
  6. Oct 27, 2005 #5
    Thanks, I understand now... I don't know why it couldn't have been explained in the book that way! So then the problem: f(3/4) if f(x)=[[1-2x]] equals -1 since [[1-2x]] turns into [[-.75]] which = -1 according to the funky [[x]] symbol!
    Thanks again,
    -Alan
     
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