What are the asymptotes and removable discontinuities, if any, of #f(x)=6/x-2#?

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Answer 1 · 2018-02-22T20:00:06

See below.

Vertical asymptotes occur where the function is undefined:

If #x=0#

#6/0-2color(white)(8888)# Undefined, division by zero

Vertical asymptote at #bb(x=0)color(white)(888)# This is the y axis

as: #x->oo# , #color(white)(888.8)6/x->0=>0-2=-2#

as: #x->-oo# , #color(white)(88)6/x->0=>0-2=-2#

So the line:

#bb(y=-2)# is a horizontal asymptote.

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