Finding the End Behaviour Model for a Power Function?

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The discussion revolves around finding the end behavior model for the power function f(x) = (2x + 1)/(x^2 - 2x + 1). Participants clarify that "end behavior model" is not standard terminology in mathematics. They agree that the function has a horizontal asymptote at y = 0, which relates to its end behavior. The conversation suggests that understanding limits as x approaches infinity and negative infinity is crucial for analyzing the function's behavior. Overall, the focus is on clarifying the concept of end behavior in relation to the given function.
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For some reason I am having problems finding a power function end behaviour model for this question:

f(x)= (2x + 1)/(x^2 - 2x + 1)

Can someone help? Thanks.
 
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"End behaviour model"? That's not standard mathematical terminology is it?

f(x)= \frac{2x+1}{(x-1)^2}

That has y= 0 as a horizontal asymptote which is how I would be inclined to interpret "end behaviour".
 
Yeah, I haven't heard of that either.

Does that mean:

\lim_{x\rightarrow{\infty}} and \lim_{x\rightarrow{-\infty}} ?
 

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