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

1 Answer
Binayaka C.
Jul 7, 2018

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]

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