question\nfind all horizontal asymptotes of the following function.\n f(x)=\frac{3 x-2}{(x+5)(3 x-2)}…

question\nfind all horizontal asymptotes of the following function.\n f(x)=\frac{3 x-2}{(x+5)(3 x-2)} \nanswer attempt 1 out of 2\none horizontal asymptote\nno horizontal asymptotes\none horizontal asymptote\ntwo horizontal asymptotes

question\nfind all horizontal asymptotes of the following function.\n f(x)=\frac{3 x-2}{(x+5)(3 x-2)} \nanswer attempt 1 out of 2\none horizontal asymptote\nno horizontal asymptotes\none horizontal asymptote\ntwo horizontal asymptotes

Answer

Explanation:

Step1: Simplify the function

Cancel out the common factor (3x - 2) (assuming (x\neq\frac{2}{3})) in the numerator and denominator. (f(x)=\frac{3x - 2}{(x + 5)(3x - 2)}=\frac{1}{x + 5}), (x\neq\frac{2}{3})

Step2: Find the limit as (x\to\pm\infty)

Use the formula (\lim_{x\to\pm\infty}\frac{a}{x + b}=0) (where (a = 1), (b=5)) (\lim_{x\to\infty}\frac{1}{x + 5}=0) and (\lim_{x\to-\infty}\frac{1}{x + 5}=0)

Answer:

One Horizontal Asymptote ((y = 0))