Answer
The graph of $h$ is a vertical translation $1$ units down of the graph of $f$.
The domain is all real numbers.
The range is $y\geq -1$.
The graph is shown below.
Work Step by Step
The given function is
$f(x)=|x|$
and
$h(x)=|x|-1$
By using input-output values prepare a table of values.
Plot the ordered pairs.
The function $h$ is of the form $y=f(x)-k$, where $k=1$.
Hence, the graph of $h$ is a vertical translation $1$ units down of the graph of $f$.
The domain is all real numbers.
The range is $y\geq -1$.