Answer
$\begin{array}{ll}
a. & 4\\
b. & 5\\
c. & 5\\
d. & |x|+4\\
e. & -|x|-4\\
f. & |x+1|+4\\
g. & 2|x|+4\\
h. & |x+h|+4
\end{array}$
Work Step by Step
$f(x)=|x|+4$
$\begin{array}{lll}
(a)\ f(0) & (b)\ f(1) & (c)\ f(-1)\quad \\
=|0|+4 & =|1|+4 & =|-1|+4\\
=4 & =5 & =5\\
& &
\end{array}$
$\begin{array}{ll}
(d)\ f(-x) & (e)\ -f(x)\\
=|-x|+4 & =-(|x|+4)\\
=|x|+4\quad & =-|x|-4\\
&
\end{array}$
$\begin{array}{ll}
(f)\ f(x+1) & (g)\ f(2x)\\
=|x+1|+4 & =|2x|+4\\
& =2|x|+4\\
& \\
&
\end{array}$
$(h)\ f(x+h)=|x+h|+4$