Graphing absolute values

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• Oct 16th 2006, 05:21 AM
^_^Engineer_Adam^_^
Graphing absolute values
help
y = |x - 6| + 6
• Oct 16th 2006, 05:41 AM
CaptainBlack
Quote:

Originally Posted by ^_^Engineer_Adam^_^
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
• Oct 16th 2006, 06:26 AM
Soroban
Hello, ^_^Engineer_Adam^_^!

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

Quote:

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!