What are the asymptotes of #y=1/(x-2)# and how do you graph the function?

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Answer 1 · 2018-05-23T12:47:50

Vertical asymptote: #x=2# and horizontal asymptote: # y=0#
Graph - Rectangular hyperbola as below.

#y = 1/(x-2)#

#y# is defined for #x in (-oo,2) uu (2,+oo)#

Consider #lim_(x->2^+) y =+oo#

And #lim_(x->2^-) y =-oo#

Hence, #y# has a vertical asymptote #x=2#

Now, consider #lim_(x->oo) y =0#

Hence, #y# has a horizontal asymptote #y=0#

#y# is a rectangular hyperbola with the graph below.

graph{1/(x-2) [-10, 10, -5, 5]}