# How do you graph y=11/(x-9)+9 using asymptotes, intercepts, end behavior?

Dec 17, 2016

The asymptotic horizontal and vertical tangents are y = 9 and x = 9, respectively. x-intercept ( y = 0 ): 88/9 and y-intercept (x = 0 ): 88/9.

#### Explanation:

Reorganizing,

$\left(x - 9\right) \left(y - 9\right)$=constant = 11.

This represents the rectangular hyperbola (RH) , having the

asymptotic tangents x-9=0=y-9 that meet at the center (9, 9) of the

RH.

As $x \to \pm \infty$, and likewise, as $y \to \pm \infty$, the RH $70$ the

respective asymptotes.

graph{(x-9)(y-9)-11=0 [-80, 80, -40, 40]}