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Math Help - Absolute Value Graph

  1. #1
    Senior Member Stroodle's Avatar
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    Absolute Value Graph

    Can someone please show me the steps for graphing f(x)=-\lvert x+3 \rvert +2

    Preferably by splitting it into two equations, one for x\geq-3 and one for x<3

    Though any other method that I can use consistently would also help.

    Thanks
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Would you be able to graph g(x)=-|x|?

    This graph should be translated along both the axes appropriately to obtain the graph of f(x).

    This link might help you: http://www.binarythings.com/graphsight/
    Last edited by alexmahone; June 16th 2009 at 01:04 AM.
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  3. #3
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by Stroodle View Post
    Can someone please show me the steps for graphing f(x)=-\lvert x+3 \rvert +2

    Preferably by splitting it into two equations, one for x\geq-3 and one for x<3

    Though any other method that I can use consistently would also help.

    Thanks

    (edit) Sorry. I just realised I put this in the wrong thread...
    first rewrite -\lvert x+3 \rvert without using the absolute value symbol you will have

    -\lvert x+3 \rvert=\left\{ \begin{array}{rcl}<br />
-x-3 & \mbox{if} & x>-3 \\ x+3 & \mbox{if} & x\leq-3<br />
\end{array}\right.

    according to this
    Absolute Value Graph-graphj.jpg

    the graph of it
    Absolute Value Graph-ex.jpg


    now f(x)=-\lvert x+3 \rvert+2

    f(x)=-\lvert x+3 \rvert+2=\left\{ \begin{array}{rcl}<br />
-x-3+2 & \mbox{if} & x>-3 \\ x+3+2 & \mbox{if} & x\leq-3<br />
\end{array}\right.


    \Rightarrow f(x)=-\lvert x+3 \rvert+2=\left\{ \begin{array}{rcl}<br />
 -x-1 & \mbox{if} & x>-3 \\ x+5 & \mbox{if} & x\leq-3<br />
 \end{array}\right.

    the graph of it like the graph above just rise it 2 unit up like this

    Absolute Value Graph-grew.jpg
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  4. #4
    Super Member
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    Smile

    Hello
    i think i have what you need
    Graphing Absolute-Value Functions

    if you want to see whether your graphing is correct or not,use this software :
    http://www.geogebra.org/download/GeoGebra_3_2_0_0.exe

    Or this one :
    SourceForge.net: Maxima -- GPL CAS based on DOE-MACSYMA: Files
    Last edited by mr fantastic; June 16th 2009 at 05:30 AM. Reason: Merged posts
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  5. #5
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    Hello, Stroodle!

    Graph: . f(x)\:=\:-|x+3| +2
    We know what: f(x) \:=\:|x| looks like.
    Code:
                      |
                  \   |   /
                   \  |  /
                    \ | /
                     \|/
          - - - - - - + - - - - - -
                      |
                      |

    Then: . f(x) \:=\:|x\:{\color{red}+\:3}\:| moves the graph 3 units to the left.
    Code:
            \       / |
             \     /  |
              \   /   |
               \ /    |
          - - - * - - + - - - - - -
               -3     |
                      |

    Then: . f(x)\:=\:{\color{red}-}|x+3| inverts the graph vertically.
    Code:
                      |
                      |
               -3     |
          - - - * - - + - - - - - -
               / \    |
              /   \   |
             /     \  |
            /       \ |
                      |

    Finally, f(x) \:=\:-|x+3| \:{\color{red}+ 2} moves the graph up 2 units.
    Code:
                      |
             (-3,2)   |
                *     |
               / \    |
        - - - / - \ - + - - - - - -
             /     \  |
            /       \ |
                      |

    There!

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  6. #6
    Senior Member Stroodle's Avatar
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    Thanks heaps for your help guys, really appreciate it. Didn't expect such detailed answers.
    I've got it now
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