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Not monotonic with increase/decrease intervals

  1. Nov 27, 2012 #1
    Hello,
    Would it be correct to say that the function y=|(x^3)-1| is not monotonic, yet increases for every x>0 and decreases for every x<0?
    I hope one of you could comment. Thanks!
     
  2. jcsd
  3. Nov 27, 2012 #2

    HallsofIvy

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    I'm not sure why you use the word "yet". Any function that "increases for every x>0 and decreases for every x<0" is NOT monotonic, by definition of "monotonic". It is true that this function, because it "increases for every x>0 and decreases for every x<0" is monotonic on x> 0 and on x< 0. But not "monotonic" for all x.
     
  4. Nov 27, 2012 #3
    Thank you, HallsofIvy, that was certainly helpful :-).
     
  5. Nov 27, 2012 #4
    Yes, but x=0 isn't the point at which decreasing turns into rising.

    Try sketching the graph of f(x)=x³, then of g(x)=x³-1, and then of h(x)=|x³-1|. A rough sketch will do, as long as you make sure you don't add "bumps" which would change the monotonicity.
     
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