Answer
Graphing as instructed, we see that
the graph of (b) is obtained by
shifting the graph of (a) to the left by 3 units.
Vertically compressing by factor $\displaystyle \frac{1}{2}$ gives graph (c), and
shifting 3 units down produces graph (d).
Work Step by Step
Taking
(a) $y=f(x)=\displaystyle \frac{1}{\sqrt{x}},$ we find that
(b) $y=f(x+3),$
(c) $y=\displaystyle \frac{1}{2}[f(x+3)]$
(d) $y=\displaystyle \frac{1}{2}[f(x+3)]-3$
So,
the graph of (b) is obtained by
shifting the graph of (a) to the left by 3 units.
Vertically compressing by factor $\displaystyle \frac{1}{2}$ gives graph (c), and
shifting 3 units down produces graph (d).