1. ## Graph sketching

How to sketch this graph ?

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

2. Everything which is negative turns positive

3. Originally Posted by thereddevils
How to sketch this graph ?

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

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

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

graph each interval with it is function

4. 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!
.

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