first off im sorry for my bad english, i especially lack "specialised" vocabulary. I hope you can still guess what im tryin to ask
So, i had a math-test yesterday, and one of the topics was curve sketching.
I think it was y=(x^2-10)/(x^2-3x-10)
I remember the limes being 3, and the poles being -2 and 5. So the curve was entering from the left above the limes, taking a left turn at the lime & left pole crossing into +infinite-y, then coming in from below, taking a turn back down (like an upside down U), and then came in again from top, taking a left at the right pole & limes crossing going to infinite-x.
Il'd draw it online somewhere but i think im not allowed to post links with the amounts of posts i have :S But i think you get the picture.
Anyways, we have to "describe" the different sides of the curve, for example:
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lim -> infinite
My question is..is there a negative infinite?
Like saying "curve comes from the left side, negative infinite x, taking a left going to a positive infinite y"?
Because from what i know, infinity can be explained like this:
If you take the number-line and draw a circle above it, every tangent relates to a number on the number-line, except for the ones that are parallel to it.
So, the infinity-tangents go from -infinite to +infinite. Does it even matter, or is it mathematically correct one way or the other, to say "-infinite" and "+infinite"? I mean, maybe if you have it in an equation and you can cancel it down, it would still leave -1...hm...
Anyways, if he strips some points because i didn't say "-infinite" and "+infinite" il'd like to be able to call bs on it (or know to just take it xD)
edit: Whoa..i just read about latex and tried to implement the \infty symbol..but that tore my text to shred, cuz it always centered it and stuff. So..sorry for not using LaTex, but i don't have the time to play around atm (@work )