Question

How do you graph `y=3/(x+8)-10` using asymptotes, intercepts, end behavior?

Answer 1

Vertical asymptote is at `x=-8` ,Horizontal asymptote is at `y=-10`, x intercept at `(-7.7,0)`, y intercept at `(0, -9.625)`, end behavior: `y-> -10` as `x -> -oo andy-> -10` as `x -> oo`

Explanation:

`y =3/(x+8) - 10 or y = (3-10 x-80)/(x+8)` or

`y = (-10 x-77)/(x+8)`

Vertical asymptote occur when denominator is zero.

`x+8=0 :. x= -8; lim(x->8^-) y -> -oo`

`lim (x->8^+) y - > oo`

Vertical asymptote is at `x=-8`

Horizontal asymptote: `lim (x->-oo) ; y =-10/1=-10`

Horizontal asymptote is at `y=-10`

x intercept: Putting `y=0` in the equation we get,

`-10 x -77=0 :. x = -7.7` or at `(-7.7,0)`

y intercept: Putting `x=0` in the equation we get,

`y= -77/8= -9.625` or at `(0, -9.625)`

End behavior: `y-> -10` as `x -> -oo` and

`y-> -10` as `x -> oo`

graph{3/(x+8)-10 [-90, 90, -45, 45]} [Ans]