Answer
$f$ is increasing on (-1,$\infty$)
Work Step by Step
Define $f(x) = | x+1 |$ as two separate cases,
When $x\leq -1$, $f(x) = -(x+1)$
$\implies$ $f'(x) = -1$, which means $f$ is decreasing
When $x>-1$, $f(x) = x+1$
$\implies$ $f'(x) = 1$, which means $f$ is increasing
