question 3 · 1 point\nwhat is the horizontal asymptote of the graph of ( f(x)=\frac{9 x^{2}+2}{x^{2}+x}…

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

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

Answer

Explanation:

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

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

Step2: Evaluate the limit

As (x\rightarrow\pm\infty), (\frac{2}{x^{2}}\rightarrow0) and (\frac{1}{x}\rightarrow0). So (\lim_{x\rightarrow\pm\infty}\frac{9+\frac{2}{x^{2}}}{1+\frac{1}{x}}=\frac{9 + 0}{1+0}=9)

Answer:

(y = 9)