Question

Identify the asymptotes.
y=1/x-6

Answer 1

Horizontal asymptote
\[\LARGE y=\frac{1}{x-6} \]
\[\LARGE \lim_{x\to\infty }=\frac{1}{x-6} =\frac{\frac 1x}{\frac xx-\frac 6x }=\frac 01=0\]
Well dude, I'm not sure, I'll go grab my notebook :$

Answer 2

Ok

Answer 3

The function is also undefined at x=6. So there is a vertical asymptote at x=6.

Answer 4

x = 6 vertical asymptote
y = 0 horizontal asymptote

Answer 5

Horizontal asymptote that I wrote above it's ok.
Vertical Asymtote:
\[\LARGE y={1\over x-6}\]
x-6=0
x=6

and asymptote which is between vertical and horizontal (I STILL don't know how to say it) ...
is:
\[\LARGE y=kx+b \quad \quad k\neq 0\]
\[\LARGE k=\lim_{x\to \infty }\frac{f(x)}{x}\]
and
\[\LARGE b=\lim_{x\to \infty}[f(x)-kx]\]

\[\LARGE k=\lim_{x\to \infty }\frac{1\over x-6 }{x}={1\over x(x-6) }=0\]
so since
\[\LARGE k\neq 0\]
and we got:
k=0
there's no asymptote like this :)

Answer 6

I think you're referring to the oblique asymptote.

Answer 7

oblique? .. let me go and translate it :F

Answer 8

whoaa... That's right. At Last. IT'S OBLIQUEEE.... :F