Help??? Can anyone clarify the difference btw an assymptote and a hole

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<p>Does anyone know the difference btw an assymptote and a hole. I always miss these questions. Help pls. I am writing the satII this jan. I am using the Sparknotes and it does not cover recursive sequence and regression.</p>

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<p>A hole is when the term is in both the nominator and the denominator. An asymptote happens when it is only in the denominator.</p>

<p>For example:
((x^2-4))/((x-2)(x+3))
After you factor out the top, x-2 is on the top and bottom of the fraction. Thus, there is a hole at x=2. However, x+3 is only on the bottom of the fraction. Thus, there is an asymptote at x=-3</p>

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<p>@latency</p>

<p>u mean that x=2 is not an asymptote ? just hole ?</p>

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<p>right. Graph it on your calculator you'll see that there is a hole at x=2 and an asymptote at x=-3</p>

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<p>0/0 engenders a hole.</p>

<h1>other than 0 / 0 = asymptote.</h1>

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<p>0/0 isn't always a hole. For example: y = sin(x) / x ...</p>

<p>A "classic" hole might be: y = x^2 for x > 0 or x < 0, undefined at x=0.</p>

<p>When I think of an asymptote, I picture the graph of the function approaching a line ... e.g., y = 1/ (x-1) approaches the vertical line x=1 as x gets close to 1.</p>