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

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Answer 1 · 2016-12-17T14:39:47

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.

Reorganizing,

#(x-9)(y-9)#=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 +-oo#, and likewise, as #y to +-oo#, the RH #70# the

respective asymptotes.

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