Answer
(a) Parent function: $f(x)=|x|$
(b) A translation of $3$ units left and translation of $5$ units down.
(c) The graph of $h$ is as shown.
(d) $h(x)=f(x+3)-5$
Work Step by Step
(a) Parent function:
$$f(x)=|x|$$
(b) The transformation is a translation of $3$ units left and translation of $5$ units down.
(c) The graph of $h$ is as shown.
(d) $h$ in terms of $f$:
$$h(x)=f(x+3)-5$$