Horizontal asymptote:can be touched or not?

[gracy]

I have gone through some sites.
http://www.freemathhelp.com/finding-horizontal-asymptotes.html
It says horizontal asymptote can not be touched or crossed
http://study.com/academy/lesson/horizontal-asymptotes-definition-rules-quiz.html &http://www.purplemath.com/modules/asymtote2.htm
According t above two horizontal asymptote can be touched r crossed
Now you tell me,what's the truth?

 

[andrewkirk]

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.

 

[andrewkirk]

 

[gracy]

Did not understand.Please elaborate.

 

[andrewkirk]

You asked whether a horizontal asymptote can be crossed. Above is a graph of a function that crosses its horizontal asymptote.

 

[Mark44]

I have gone through some sites.
http://www.freemathhelp.com/finding-horizontal-asymptotes.html
It says horizontal asymptote can not be touched or crossed

You didn't read the above carefully enough. It also says this (emphasis added):

However, I should point out that horizontal asymptotes may only appear in one direction, and may be crossed at small values of x.

Horizontal asymptotes describe the behavior of a graph for large or very negative values of the dependent variable.

http://study.com/academy/lesson/horizontal-asymptotes-definition-rules-quiz.html &http://www.purplemath.com/modules/asymtote2.htm
According t above two horizontal asymptote can be touched r crossed
Now you tell me,what's the truth?