Question

question 3 · 1 point
what is the horizontal asymptote of the graph of ( f(x)=\frac{9 x^{2}+2}{x^{2}+x} )?
give your answer in the form ( y=a ).
provide your answer below:

Explanation:

Step1: Divide numerator and denominator by \(x^{2}\)

$$\lim_{x ightarrow\pm\infty}\frac{9x^{2}+2}{x^{2}+x}=\lim_{x ightarrow\pm\infty}\frac{9+\frac{2}{x^{2}}}{1 + \frac{1}{x}}$$

Step2: Evaluate the limit

As \(x
ightarrow\pm\infty\), \(\frac{2}{x^{2}}
ightarrow0\) and \(\frac{1}{x}
ightarrow0\). So \(\lim_{x
ightarrow\pm\infty}\frac{9+\frac{2}{x^{2}}}{1+\frac{1}{x}}=\frac{9 + 0}{1+0}=9\)

Answer:

\(y = 9\)