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Math Help - how to draw this function?

  1. #1
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    how to draw this function?

    \frac{3-3 ^{x}}{ \left|3-3 ^{x} \right| }  \cdot  \frac{3 ^{x} }{3 ^{ \left|x \right| } }
    Last edited by achacy; October 14th 2008 at 05:24 AM.
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  2. #2
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    Quote Originally Posted by achacy View Post
    [HTML]\frac{3-3 ^{x}}{ \left|3-3 ^{x} \right| } \cdot \frac{3 ^{x} }{3 ^{ \left|x \right| } }[/HTML]
    f(x) = \frac{3-3 ^{x}}{ \left|3-3 ^{x} \right| }  \cdot  \frac{3 ^{x} }{3 ^{ \left|x \right| } }

    1. D = \mathbb{R} \setminus \{1\}

    2.  \dfrac{3-3 ^{x}}{ \left|3-3 ^{x} \right| } = \left\{\begin{array}{r}-1 \ if \ x > 1 \\ 1 \ if \ x < 1 \end{array}\right.

    3. \dfrac{3^x}{3^{|x|}} = \left\{\begin{array}{r} 1\ if\ x \geq 0 \\ -1\ if\ x<0\end{array}\right.

    Thus you have 3 different intervals:

    f(x)=\left\{\begin{array}{ccr}1 \cdot (-1) & if & x<0 \\ 1 \cdot (+1) & if & 0 \leq x < 1 \\ (-1) \cdot (+1) & if & x>1\end{array} \right.

    I assume that you now can draw the graph.
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  3. #3
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    Quote Originally Posted by earboth View Post
    [tex]

    3. \dfrac{3^x}{3^{|x|}} = \left\{\begin{array}{r} 1\ if\ x \geq 0 \\ -1\ if\ x<0\end{array}\right.
    But I think if x<0 \frac{3 ^{x} }{ 3^{ \left| x\right| } } =3 ^{2x}

    isn't it so?
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  4. #4
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    Quote Originally Posted by achacy View Post
    But I think if x<0 \frac{3 ^{x} }{ 3^{ \left| x\right| } } =3 ^{2x}

    isn't it so?
    Almost!

    First of all: You are right: My result wasn't correct but ...

    Let x = -2 then \dfrac{3 ^{-2} }{ 3^{ \left|-2 \right| } } =\dfrac{\frac1{3 ^2}}{3^{|-2|}} = \dfrac1{3^{2+ 2}}

    In general: \dfrac{3 ^{x} }{ 3^{ \left| x\right| } } =3 ^{-2|x|}\ if \ x<0


    EDIT: I've attached the graph of the function.
    Attached Thumbnails Attached Thumbnails how to draw this function?-graph_archacy.png  
    Last edited by earboth; October 14th 2008 at 10:21 PM.
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