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

1 Answer
Tony B
Jul 28, 2016

See explanation

Explanation:

color(blue)(x_("intercept") -> 6(x-2)=6 -> x=3)xintercept→6(x−2)=6→x=3

color(blue)(y_("intercept") -> 6/(0+2)-6 =y -> y=-3)yintercept→60+2−6=y→y=−3
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Excluded value ->x=-2→x=−2 as undefined at 6/060 'not allowed'.

color(blue)(=>"Vertical Asymptote "->x=-2)⇒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 BTony B

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