I used my definition of "part of" since you never gave me one, and I'm not saying it's the mathematical definition since I have never used that phrase before but nonetheless, I assumed you meant for something to be "part of" a function it needs to touch the function, an asymptote is a tangent to the function at infinity, if it's tangent, then it touches the function (albeit at infinity), hence it is "part of" the function. Again like I said, I want to avoid this in total because I don't want to start a controversial debate on what defines infinity.
If you disagree, which you will obviously, then please enlighten me with your mathematical definition of "part of", if not, my previous solution suffices.
You guys are making a meal of a simple question. Here is a more tangible explanation of TT's solution (without using controversial words like 'infinity', 'part of', 'cut' etc.):
The only hyperbola that's an even function is constant, so =c)
is constant. Now =p)
but clearly =\lim_{x\to \infty} c=c)
so 
I thought you said not using infinity.
If you want be pedantic, pretend kamil only said
The only hyperbola that's an even function is constant
...which you seem to have a hard time interpreting too from your previous post.
When I said in my few previous posts before about the only way to make the hypebola even is analogous to what kamil just stated.
However only one part of any hyperbola is even, that is it's horizontal asymptote
and never did I state that the asymptote had to the "part of" the function
just happens p = horizontal asymptote
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