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Math Help - Trying to understand these functions...

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    2

    Trying to understand these functions...

    I have two functions that I'm not quite sure how to deal with, if I could imagine their graphs I'd be fine but I can't I've looked everywhere for a simple explanation, now I'm looking here =]

    --------sin(pi*x/2)--------[0,2]
    f(x) = { 0----------------[2,4]
    --------f(x+4)

    I have no idea what the square brackets are trying to tell me here =/


    --------0---------1 < x < 0
    f(x) = { 1/2-------x=n--------nEz
    --------1--------0 < x < 1
    --------f(x+2)

    Again, I'm not quite sure how to read this. Anyone help me??
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
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    Hello, Stuckasaurus!

    f(x) \;=\;\begin{Bmatrix}\sin\left(\frac{\pi}{2}x\right  ) & [0,2] \\ \\[-4mm] 0 & [2,4] \\ f(x+4) & {\color{red}?}\end{Bmatrix}
    I'm not sure what that third entry means.
    It probably means that this graph is repeated over and over,
    . . but I'll graph just one "cycle".

    The brackets indicate intervals.
    . . [0,2] means: . 0 \leq x \leq 2

    Brackets mean the endpoints are included.

    If the endpoints are not included, parentheses are used.
    . . (1,3) means: .  1 < x < 3

    And, yes, they can be "mixed".
    . . (0, 4] means: .  0 < x \leq 4


    This problem says:

    If 0 \leq x \leq 2, the graph is a sine function: . y \:=\:\sin\left(\frac{\pi}{2}x\right)

    If 2 \leq x \leq 4, the graph is y \:=\:0 ... the x-axis.

    The graph looks like this:
    Code:
            |
           1+       *
            |   *       *
            | *           *
            |*             *
            |
        - - * - - - - - - - * * * * * * * * * - -
            |               2               4

    f(x) \;=\;\begin{Bmatrix}0 & -1 < x < 0 \\ \\[-4mm]<br />
\frac{1}{2} & x \in Z \\ \\[-4mm] 1 & 0 < x < 1 \\ f(x+2) & {\color{red}?}\end{Bmatrix}

    This function says:

    If x is between -1 and 0, the graph is y = 0, the x-axis.

    If x is an integer, the graph is .

    If x is between 0 and 1, the graph is y = 1


    And the graph looks like this:
    Code:
                    | 
                   1o=======o
                    |
                    *
                    |
        - - o=======o - - - + - -
           -1       |       1
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  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    2
    Wow, you're like.. better than my lecturer! Thanks soooo much =]
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