Finding Asymptotes

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I'm stuck at understanding why +c is the horizontal asymptote. Can someone please explain this? I get that the vertical asymptote is relating to (x+b), because the denominator cannot=0. But why does this kind of graph have a horizontal asymptote to begin with? enter image description here

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  • If $a$ and $b$ are reasonably-sized and $x=1000$, then what is the fraction $\dfrac{a}{(x+b)^2}$ approximately equal to?
  • What about if $x=-1000$?
  • Using the two facts above, what is $y=\dfrac{a}{(x+b)^2}+c$ approximately equal to for $x=\pm1000$?

This is the sort of idea you should have in mind when looking for non-vetical asymptotes (in particular, horizontal ones).