Question 977095
As given in plain text, f(x)= 1/x-6


Rendering the function, {{{f(x)= 1/x-6}}}


DOMAIN:  The one value of x not acceptable is x=0.
The domain is all real numbers so that {{{x<>0}}}.


The undefined x at 0 gives a vertical asymptote at x=0.


f seems to approach  -6 when x goes unbounded in either direction.
The rational term approaches 0, making the result easy to see or visualize.
Horizontal asymptote, y=-6.


NO VERTICAL AXIS INTERCEPT.  Review the discussion given earlier.


What do you find if y=0?
{{{1/x-6=0}}}
{{{1/x-6x/x=0}}}
{{{(1-6x)/x=0}}}
{{{1-6x=0}}}---because the denominator does not control any of this.
{{{1=6x}}}
{{{x=1/6}}}------the x-axis intercept.



{{{graph(300,300,-10,10,-13,7,1/x-6)}}}