Determine the equation of the horizontal asymptotes, if any, of the function.
g(x)=(x+3)/((x+1)(x-2))

Question

Determine the equation of the horizontal asymptotes, if any, of the function.
g(x)=(x+3)/((x+1)(x-2))

haleyelizabeth2017 · Answer

$$g(x)=\frac{ x+3 }{ (x+1)(x-2) }$$

haleyelizabeth2017 · Answer

Would the horizontal asymptote be y=0? Or...?

jim_thompson5910 · Answer

what is the degree of the numerator? degree of the denominator?

anonymous · Answer

yes

haleyelizabeth2017 · Answer

I expanded the denominator to get $x^2-x-2$

anonymous · Answer

the degree of the denominator is larger than the degree of the numerator

jim_thompson5910 · Answer

the actual expansion doesn't matter. The key here is that we have x^2 as the first term, so we have a 2nd degree polynomial in the denominator

haleyelizabeth2017 · Answer

Okay

anonymous · Answer

this is not a mystery.
plug in say $x=100$ (not a hysterically large number) and see that you get an answer very close to zero

haleyelizabeth2017 · Answer

Okay.  Thank you both :)