Answer
\[y = - 1{\text{ and }}y = 1{\text{ are both horizontal asymptotes}}\]
Work Step by Step
$$\eqalign{
& f\left( x \right) = \frac{{\left| x \right|}}{{x + 1}} \cr
& {\text{From the graph we have:}} \cr
& \mathop {\lim }\limits_{x \to - \infty } \frac{{\left| x \right|}}{{x + 1}} = - 1{\text{ and }}\mathop {\lim }\limits_{x \to \infty } \frac{{\left| x \right|}}{{x + 1}} = 1 \cr
& {\text{Then,}} \cr
& y = - 1{\text{ and }}y = 1{\text{ are both horizontal asymptotes}} \cr} $$
