Question

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

Answer 1

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)`