<p>Hi, I'd really appreciate if somebody helped me out with this problem. I seem to be getting a different result than sparknotes and as the test is in two days, it would calm my nerves to know where (or if) I'm wrong.</p>
<p>The Q goes like this:</p>
<p>How many vertical asymptotes does the graph of (x-3)/ ((x+2)(x2-9)) have?</p>
<p>Logically, I chose three, as I (together with my calculator) would say that they occur at -2, 3, -3. However, sparknotes says that they are only -2 and -3 as 3 crosses out during simplification. </p>
<p>I understand I could simplify it but if I type it into my calc, y is undefined for all three of them. Can anybody please tell me where is the mistake?</p>
<p>Yep, asymptote is where the graph tends to infinity, so you have to see the limit, and for limits, you have to bring the expression in the reduced form
which is
(x-3)/(x+2)(x+3)(x-3)
= 1/(x+2)(x+3)</p>
<p>another way is that, when you put 3, both numerator and denominator become 0.. and 0/0 is not infinity (vertical asymptote) but 'indeterminate' form..the graph ceases to exist at that point.</p>
<p>Thank you very much, now I see:) I was wondering why the calculator showed vertical lines only for the two x values.
Do you think I can rely on my calc to verify my answer in such questions? I mean if there was no vertical asymptote shown on the grapher, can I be sure that there really is none?</p>
<p>Not really... The calculator doesn't work too good for certain functions, like tan x. (the earlier software versions). But yeah, in general you can trust the calccy!</p>
<p>well, not few:) in test nr three I found five of them (wrongly set questions, inconstant with the solutions) and nrs 4 and 5 are totally messed up in terms of scoring and correct/incorrect answers, they always show you got 0/50 correct (and I'm not that bad at math:)...</p>