Results 1 to 4 of 4

Math Help - Absolute Value Graphs

  1. #1
    Senior Member
    Joined
    Jul 2008
    Posts
    347

    Absolute Value Graphs

    Hi

    For y = abs(x+2) + abs(x) + abs(x-2), what are the cases?

    I know if there were only two abs, there would be three cases to work out but I have no clue how many there will be for this question and what they might be.

    Thanx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2008
    Posts
    111
    Dear xwrathbringerx,

    the abs(x) function behaves "irregular" at x=0 that is x=0 is a singular point.
    Therefore the function abs(x-2) has sigularity at x=2, hasn't it?

    So in your problem you have to divide into 4 cases because there are 3 singular point.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2007
    Posts
    329
    If x\le -2 then y=-(x+2)-x-(x-2)=-3x.
    If -2\le x\le 0 then y=(x+2)-x-(x-2)=-x+4.
    If 0\le x\le 2 then y=(x+2)+x-(x-2)=x+4.
    If 2\le x then y=(x+2)+x+(x-2)=3x.

    The graph is attached.
    Attached Thumbnails Attached Thumbnails Absolute Value Graphs-abs.png  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,802
    Thanks
    692
    Hello, xwrathbringerx!

    Another approach . . .


    For y \:=\:|x+2| + |x| + |x-2|, what are the cases?
    Make a sketch . . .

    The graph of . y \,=\,|x| .is a \vee with its vertex at the origin.

    The graph of . y \,=\,|x-2| .is the same graph moved 2 units to the right.

    The graph of . y \,=\,|x+2| .is the same graph moved 2 units to the left.

    Code:
          \    \    |    /    /
           \    \   |   /    /
            \    \  |  /    /
             \    \ | /    /
              \    \|/    /
          \    \    *    /    /
           \    \  /|\  /    /
            \    \/ | \/    /
             \   /\ | /\   /
              \ /  \|/  \ /
      ---------*----*----*-------
              -2    |    2

    Then add the ordinates.

    We get the graph that james_bond so thoughtfully provided.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. absolute value graphs
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 19th 2010, 12:11 PM
  2. Absolute value graphs
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 14th 2009, 08:23 AM
  3. Absolute Value Graphs
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 22nd 2008, 01:50 AM
  4. graphs absolute
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: December 8th 2006, 05:15 AM
  5. absolute value graphs
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 1st 2006, 03:00 PM

Search Tags


/mathhelpforum @mathhelpforum