Graph sketching

**thereddevils** · June 18th 2009, 03:11 AM

How to sketch this graph ?

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

**Rachel.F** · June 18th 2009, 03:46 AM

Everything which is negative turns positive

**Amer** · June 18th 2009, 03:50 AM

Originally Posted by thereddevils

How to sketch this graph ?

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

$3+\frac{1}{x} =0$

$x =\frac{-1}{3}$

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

graph each interval with it is function

**Soroban** · June 18th 2009, 04:17 AM

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!
.

**thereddevils** · June 18th 2009, 06:08 AM

Oh yeah , i have to find the vertical and horizontal asymtote first .. THanks a lot guys .

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