find the equation of all horizontal asymptotes of the following function.\nf(x)=\\frac{24}{5x}-6\nanswer…

Explanation:

Step1: Recall the rule for horizontal asymptotes

For a rational function (y = \frac{a}{x}+b) (where (a\neq0)), we find the limit as (x\to\pm\infty). The formula for horizontal asymptote is (y = \lim_{x\to\pm\infty}f(x)).

Step2: Calculate (\lim_{x\to\pm\infty}f(x))

We know that (\lim_{x\to\pm\infty}\frac{24}{5x}=0) (since (\lim_{x\to\pm\infty}\frac{c}{x}=0) for any constant (c)). Then (y=\lim_{x\to\pm\infty}(\frac{24}{5x}-6)). Using the limit property (\lim_{x\to a}(u(x)+v(x))=\lim_{x\to a}u(x)+\lim_{x\to a}v(x)), we have (y = 0 - 6).

Answer:

One Horizontal Asymptote, (y=-6)