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

Question

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

anonymous · Answer

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

anonymous · Answer

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: $$f(x)=\frac{ x^2-3x+2 }{ x+10 }$$

anonymous · Answer

so none would be the answer?

anonymous · Answer

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.

anonymous · Answer

Check my previous replies again.

anonymous · Answer

I already gave you an example. :D

anonymous · Answer

okay thank you