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Math Help - Graph sketching

  1. #1
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    Graph sketching

    How to sketch this graph ?

     y=|3+\frac{1}{x}|
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  2. #2
    Junior Member Rachel.F's Avatar
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    Everything which is negative turns positive
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  3. #3
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by thereddevils View Post
    How to sketch this graph ?

     y=|3+\frac{1}{x}|
      3+\frac{1}{x}  =0

     x =\frac{-1}{3}


    Graph sketching-abslo.jpg


    \left\{ \begin{array}{rcl}<br />
3+\frac{1}{x} & \mbox{if} & x<\frac{-1}{3} \\[3mm] -3-\frac{1}{x} & \mbox{if} & \frac{-1}{3}\leq x <0 \\[3mm] 3+\frac{1}{x} & \mbox{if} & x>0<br />
\end{array}\right.

    graph each interval with it is function
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  4. #4
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    Hello, thereddevils!

    How to sketch this graph: .  y\:=\:\left|3+\frac{1}{x}\right|
    First, graph: . y \;=\;3 + \frac{1}{x}
    Code:
                        |
                        |*
                        |
                        | *
                        |  *
                        |    *
                        |        *
                       3|             *
        - - - - - - - - + - - - - - - - - -
          *             |
               *        |
      -------------*----+--------------------
                     *  |
                      * |
                        |
                       *|
                        |

    Then anything below the x-axis is reflected upward.

    Code:
                        |
                        |*
                        |
                       *| *
                        |  *
                        |    *
                        |        *
                       *|             *
        - - - - - - - - + - - - - - - - - -
          *           * |
               *     *  |
      -------------*----+--------------------
                        |
                        |
                        |
    Edit: Ah . . . Rachel.F beat me to it!
    .
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  5. #5
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    Oh yeah , i have to find the vertical and horizontal asymtote first .. THanks a lot guys .
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