Question

What is the equation of the horizontal asymptote of function $f\left(x\right)=\frac{2}{(x+2)}-\frac{(x+3)}{(x+4)}$?

• A. $-4$
• B. $-2$
• C. $-1$
• D. $0$

Answer 1

The correct option is C $-1$

$y=(\frac{2}{x+2}-\frac{x+3}{x+4})$

$y=(\frac{2}{x+2}-\frac{3}{x+4}-\frac{x}{x+4})$

$horizontal$ $asymptote,$

line $y=L$ is a horizontal asymptote of fuction if either ${}_{x\to \infty }^{lim}f\left(x\right)=L$ and ${}_{x\to \infty }^{lim}f\left(x\right)=L$

where $L$ is finite

${}_{x{\to }_{-}^{+}\infty }^{lim}(\frac{2}{x+2}-\frac{3}{x+4}-\frac{x}{x+4})=-1$

hence equation of horizontal asymptote is $y=-1$