## anonymous one year ago State the horizontal asymptote of the rational function. f(x) = quantity x plus nine divided by quantity x squared plus two x plus three.

1. anonymous

$f(x)=x+9/x ^{2}+2x+3$ is the equation

2. anonymous

If the degree of the first term in the numerator is lower than the degree of the first term of the denominator, then the horizontal asymptote is y=0. Example: $f(x)=\frac{ x+2 }{ x^2-3x+2 }$ BUT If the degree of the first term in the numerator is higher than the degree of the first term of the denominator, then the horizontal asymptote is none. Example: $f(x)=\frac{ x^2-3x+2 }{ x+10 }$

3. anonymous

so none would be the answer?

4. anonymous

HOWEVER If the degree are the same in both numerator and denominator, you have to divide the coefficient of the first degree of the term of he numerator to the denominator's. Example: $f(x)=\frac{ 2x^2-11 }{ x^2+9 }$ The horizontal slope here is y=2.

5. anonymous

Check my previous replies again.

6. anonymous

I already gave you an example. :D

7. anonymous

okay thank you