Horizontal Asymptotes


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A horizontal asymptote is a y-value on a graph which a function approaches but does not actually reach. Here is a simple graphical example where the graphed function approaches, but never quite reaches, \(y=0\). In fact, no matter how far you zoom out on this graph, it still won't reach zero. However, I should point out that horizontal asymptotes may only appear in one direction, and may be crossed at small values of x. They will show up for large values and show the trend of a function as x goes towards positive or negative infinity.



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