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Horizontal asymptote:can be touched or not?

  1. Oct 25, 2015 #1
  2. jcsd
  3. Oct 25, 2015 #2

    andrewkirk

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    Here is a picture of a horizontal asymptote that is crossed. The function is ##f(x)=e^{-x}(0.5+e^{-x}\sin 10x)##. The curve crosses the asymptote in both directions, then remains above it as it approaches from above.
     
  4. Oct 25, 2015 #3

    andrewkirk

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    upload_2015-10-25_20-11-14.png
     
  5. Oct 25, 2015 #4
    Did not understand.Please elaborate.
     
  6. Oct 25, 2015 #5

    andrewkirk

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    You asked whether a horizontal asymptote can be crossed. Above is a graph of a function that crosses its horizontal asymptote.
     
  7. Oct 27, 2015 #6

    Mark44

    Staff: Mentor

    You didn't read the above carefully enough. It also says this (emphasis added):
    Horizontal asymptotes describe the behavior of a graph for large or very negative values of the dependent variable.
     
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