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Please help about sketching graphs

  1. Nov 29, 2004 #1
    I want to ask you an exam question about sketching graph of a function, please help me;

    I want you to look at question 2 from the following link especially 2 d)(about asymptotes)


    question


    and the solutions given by the department are here;


    solutions


    what i did not understand is that; i think y=0 line must be another horizontal asymptote .Am ı wrong???

    thank you for your helps...
     
  2. jcsd
  3. Nov 29, 2004 #2

    HallsofIvy

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    I don't understand WHY you think that y=0 "must be another horizontal asymptotote".

    In order for y= k to be a horizontal asymptote for any function, the graph must approach that line as x goes to either +infinity or -infinity. In this case, the derivative, to the right of x= 1 IS the constant -4 so the graph is the line y= -4.
    There is no reason to think that the derivative approaches any constant, much less 0, as x goes to -infinity.
     
  4. Nov 29, 2004 #3
    I looked at the description of horizontal asymptote , so you're right the derivative does not approach any constant but as x goes to - infinity the derivative is always less than zero and always increasing , I thought that could be counted as asymptote.

    I have description of horizontal asymptote:

    "the graph of f(x) has a horizontal asymptote y=L if
    lim x-->infinity f(x)=L" is this true?

    and in the question "lim x--> - infinity f(x)=0" is this wrong?

    must the graph reach a constant as you said , to be a hor. asy.?

    thank you for your help...
     
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