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]}

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