Chapter SH, Problem 11.2.2EP

To determine

The asymptotes of the given rational function.

Answer to Problem 11.2.2EP

Vertical asymptote:

  $x=-3$

Horizontal asymptote:

  $y=1$

Explanation of Solution

Given:

The given function is:

  $f\left(x\right)=\frac{x-2}{x+3}$

Calculation:

A rational function $f\left(x\right)=\frac{a}{x-b}+c$ has:

Vertical asymptote = $x-b=0$

Horizontal asymptote = $y=c$

Therefore, the asymptotes of the given function will be:

Vertical asymptote:

  $\begin{array}{l}x+3=0\\ x=-3\end{array}$

Horizontal asymptote:

  $y=1$