How do you find all the asymptotes for function #y=2/(x-1)+ 1#?

1 Answer
Jan 16, 2016

Answer:

First you make the denominator go to zero, later you make #x# go to infinity.

Explanation:

The first happens when #x# goes down to 1 and #y# will get larger and larger, or in the language:
#lim_(x->1+) y=oo#
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We also have #x# going up to 1 and #y# will be larger but negative:
#lim_(x->1-) y=-oo#

The second happens when #x# goes very large, either positive or negative. The first part will the go to #0# #y# will go to #1#
#lim_(x->+-oo) y=1#

Answer: #x=1andy=1#
graph{2/(x-1)+1 [-20.27, 20.26, -10.14, 10.13]}