How do you graph #y=6/(x+2)-6# using asymptotes, intercepts, end behavior?

1 Answer
Jul 28, 2016

Answer:

See explanation

Explanation:

#color(blue)(x_("intercept") -> 6(x-2)=6 -> x=3)#

#color(blue)(y_("intercept") -> 6/(0+2)-6 =y -> y=-3)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Excluded value #->x=-2# as undefined at #6/0# 'not allowed'.

#color(blue)(=>"Vertical Asymptote "->x=-2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#lim_(x->+-oo) 6/(x+2) -> 0#

So #color(blue)(lim_(x->+-oo) y" "=" " lim_(x->+-oo)6/(x+2)-6" " =" "-6)#

Tony B