Question

give the equations of any horizontal asymptotes for the function below.
$f(x)=\frac{x^{2}+3 x - 9}{x - 9}$
$y = 2$
$y=-3$
$y = 9$
none

Explanation:

Step1: Determine the degrees of numerator and denominator

The degree of the numerator \(n = 2\) (since the highest - power term in \(x^{2}+3x - 9\) is \(x^{2}\)), and the degree of the denominator \(m=1\) (since the highest - power term in \(x - 9\) is \(x\)).

Step2: Apply the rule for horizontal asymptotes

When \(n>m\) (where \(n\) is the degree of the numerator and \(m\) is the degree of the denominator), there is no horizontal asymptote.

Answer:

none