The reciprocal function $g(x) = \frac{1}{|x + 1|}$ has several key characteristics, which include its domain, range, asymptotic behavior, and graph shape. Here’s a breakdown of these features:

1. Domain

The domain of $g(x)$ is all real numbers except where $f(x) = |x + 1| = 0$, which occurs at $x = -1$. This means $g(x)$ is undefined at $x = -1$, resulting in: $x \in (-\infty, -1) \cup (-1, \infty)$

2. Range

Since $|x + 1|$ is always non-negative,