Confused . y=x-|x|

  1. confused ..... y=x-|x|

    The problem is to graph this equation y=x-|x|.

    From what I understand of absolute values, this x would be positive. If it is positive then y=0 and there would be no points to graph. Is there something that I am missing? The question is worth 4 points, so I can't see the answer just being 0. Thanks for any suggestions.
  2. jcsd
  3. D H

    Staff: Mentor

    What happens when x is negative?
  4. What I was taught to do when dealing with absolute value, is to rewrite the equation so that the absolute value is isolated, then find the 2 equations.

    so you'll have:

    and also:
  5. The absolute value of -x would be x. But I remember with inequalities there are 2 possible answers with absolute value (-,+). From what you are explaining it sounds like that is what you are saying to do, use both possible values. Then I would graph by beginning with y at 0 and continue by substituting values into 2x=y? That seems to make sense to me. Thank you both for your help!
  6. Also just try plugging in some numbers:
    For 2 -> Y = 2 - |2| = 0
    For -2 - > Y = -2 -|-2| = -2 -2 = -4
    So for negatives you have Y = 2X, X<0
  7. symbolipoint

    symbolipoint 3,427
    Homework Helper
    Education Advisor
    Gold Member

    Solve or graph y = x - |x|.

    If x>0, then y = x - x, meaning y=0.

    If x<0, then y = x - (-x) [ notice those are parentheses, not absolute value notation symbols ], meaning y = x + x = 2x.
  8. HallsofIvy

    HallsofIvy 41,264
    Staff Emeritus
    Science Advisor

    Surely you didn't mean to say that! x itself can be any number. |x| is always positive (or 0- don't forget that!

    Why did you switch to x=? If x[itex]\ge 0[/itex] y= x- x= 0. The graph is just the x axis from x= 0 to the right.

    If x< 0, don't forget that. Then y= x- (-x)= 2x.

    No, no, no! |-x|= |x| which may be eigther x or -x depending upon what x is.

    Draw the graph of y= 2x, to the left of x= 0. To the right, the graph is just y= 0, the x-axis.
  9. I rearranged the formula to isolate the absolute value.
  10. Wow, you guys couldn't have made it any more clear for me. Thanks alot!
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