How do you find the vertical, horizontal or slant asymptotes for #y = 3/(x + 4)#?

1 Answer
May 31, 2016

Answer:

Vertical asymptote is #x=-4#
Horizontal asymptote is #y=0#

Explanation:

The equation is undefined at #x=-4# as #1/(x-4)->1/0# and division by 0 'is not allowed'. So excluded value is #x=-4#

This #x=-4# is a vertical asymptote.
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As the magnitude of #x# increases in both the positive and negative directions then #|x+4|# becomes so large that #3/(x+4)# becomes exceptionally small.

Thus

#lim_(x->-4) 3/(x+4) = +-0#

Tony B