find all horizontal asymptotes of the following function.\n\n$f(x)=\\frac{x^{2}-11x + 24}{2x^{2}-16x}$\n\nans…

Explanation:

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

$$\lim_{x\rightarrow\pm\infty}\frac{x^{2}-11x + 24}{2x^{2}-16x}=\lim_{x\rightarrow\pm\infty}\frac{1-\frac{11}{x}+\frac{24}{x^{2}}}{2-\frac{16}{x}}$$

Step2: Apply limit properties

As (x\rightarrow\pm\infty), (\lim_{x\rightarrow\pm\infty}\frac{1}{x}=0) and (\lim_{x\rightarrow\pm\infty}\frac{1}{x^{2}} = 0). So (\lim_{x\rightarrow\pm\infty}\frac{1-\frac{11}{x}+\frac{24}{x^{2}}}{2-\frac{16}{x}}=\frac{1 - 0+0}{2-0})

Answer:

(y=\frac{1}{2})