just because a factor in the denominator = 0 , that does not mean there is always a vertical asymptote there ...
have you considered point discontinuities?
Hello there budding Mathematicians! (hope i spelled that right)
Here is a quick snappy solution to vertical asymptotes, and trust me, it SUPA EASY!!
The post will probably be REALLY small (cuz its so ez).. Here we go!
Some General History: Asymptotes were created by..... Naaaah lets skip to the math.
How do you calculate them:
Simple! Let this be your function:
a can be any equation eg. ax2+bx+c or even simply x+b.. it can be anything
b can also be any equation... but its the thing that replaces b (the equation at b) that it important...
Now, to get the asymptote, simply grab the equation at b, e.g the denominator of the function (b) was x-1.
So we take that equation and simply add '= 0' to it...
x-1 = 0
.... TADAAAA.. Now simply solve for x and BOOM you got your asymptote!!!
One more example..
y = x2+2x-3/x2-5x-6
In this case, our 'b' is x2-5x-6... so we grab it and put an '= 0' at the end..
x2-5x-6 = 0..
(x-6)(x+1) = 0
x=6 or x=-1
BOOM you got your asymptotes
Well folks, thats about it! Comment if you got any questions!