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Exploring a function f(x) with absolute value

  1. Jan 27, 2009 #1
    when i am exploring a function eg. f(x)=|2x-6|

    can i treat it as two seperate function all the way through, one to the left of x=3 and one to the right, and only at the very end, when i draw the graph connect them, ie draw a graph according to all the values i found from each side? will this work whenever i have absolute value of a basic polynom, should this always come out as a mirror image?
     
  2. jcsd
  3. Jan 27, 2009 #2

    Mark44

    Staff: Mentor

    Yes. You won't have to connect them at the end, since the two halves will already be connected at x = 3.
    Yes, if you mean the mirror image across the x-axis. Take for example the function g(x) = |x^2 - 2x|. For x < 0 or x > 2, the graph looks exactly like that of the parabola y = x^2 - 2x. However, for 0 < x < 2, the portion of the graph of the parabola that lies below the x-axis is relected across it.
     
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