How do you find the asymptotes for #g(x)=(x+7)/(x^2-4)#?

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Answer 1 · 2016-01-12T00:16:15

Vertical aymptotes: #x=+-2#
Horizontal asymptotes: #y=0#

Vertical asymptotes:

These occur when the denominator equals #0#.

#x^2-4=0#

#(x+2)(x-2)=0#

#x=-2color(white)(sss)"or"color(white)(sss)x=2#

Horizontal asymptotes:

Since the degree of the denominator is larger than the numerator, the horizontal asymptote will be at #y=0#.

Graphed:

graph{(x+7)/(x^2-4) [-11.01, 11.49, -5.9, 5.35]}