## haleyelizabeth2017 one year ago Determine the equation of the horizontal asymptotes, if any, of the function. g(x)=(x+3)/((x+1)(x-2))

1. haleyelizabeth2017

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

2. haleyelizabeth2017

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

3. jim_thompson5910

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

4. anonymous

yes

5. haleyelizabeth2017

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

6. anonymous

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

7. jim_thompson5910

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

8. haleyelizabeth2017

Okay

9. anonymous

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

10. haleyelizabeth2017

Okay. Thank you both :)