Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

yes

Answer 5

I expanded the denominator to get \(x^2-x-2\)

Answer 6

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

Answer 7

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

Answer 8

Okay

Answer 9

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

Answer 10

Okay. Thank you both :)