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Math Help - Graphing absolute values

  1. #1
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    Graphing absolute values

    help
    y = |x - 6| + 6
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    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
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  3. #3
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    Hello, ^_^Engineer_Adam^_^!

    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!

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