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

Jul 7, 2018

Vertical asymptote is at $x = - 8$ ,Horizontal asymptote is at $y = - 10$, x intercept at $\left(- 7.7 , 0\right)$, y intercept at $\left(0 , - 9.625\right)$, end behavior: $y \to - 10$ as $x \to - \infty \mathmr{and} y \to - 10$ as $x \to \infty$

#### Explanation:

$y = \frac{3}{x + 8} - 10 \mathmr{and} y = \frac{3 - 10 x - 80}{x + 8}$ or

$y = \frac{- 10 x - 77}{x + 8}$

Vertical asymptote occur when denominator is zero.

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

$\lim \left(x \to {8}^{+}\right) y - > \infty$

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,

$- 10 x - 77 = 0 \therefore x = - 7.7$ or at $\left(- 7.7 , 0\right)$

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

$y = - \frac{77}{8} = - 9.625$ or at $\left(0 , - 9.625\right)$

End behavior: $y \to - 10$ as $x \to - \infty$ and

$y \to - 10$ as $x \to \infty$

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