1. Graphing absolute values

help
y = |x - 6| + 6

help
y = |x - 6| + 6
First look at the function

y=|x-6|,

when x>=6; (x-6) is >=0 so y=x-6

when x<6 (x-6) is negative so y=-(x-6)

but our y is 6 greater then the y we have looked at above so:

y.= x-6+6, ..when x>=6
..= -x+6+6, when x<6

or:

y.= x, ........when x>=6
..= -x+12, ..when x<6

which you should be able to sketch.

RonL

This is easy if you're familiar with "translations".

Graph: y .= .|x - 6| + 6

We know that the graph of: y = |x| looks like this:
Code:
              |
*       |       *
*     |     *
*   |   *
* | *
- - - - - * - - - - -
|

The graph of: y = |x - 6| is moved 6 units to the right.
Code:
              |
|   *               *
|     *           *
|       *       *
|         *   *
- - - - | - - - - - * - - - - -
|           6

Then: y = |x - 6| + 6 has been moved up 6 units.
Code:
              |
|   *               *
|     *           *
|       *       *
|         *   *
6+           *
|
|
|
- - - - + - - - - - + - - - - - -
|           6

There!