Answer
(a) to D,
(b) to D,
(c) to C,
(d) to B,
(e) to C,
(f) to C,
(g) to C,
(h) to D,
(i) to D,
(j) to C,
Work Step by Step
(a) to D, Domain of $f=\sqrt x+3$ is $x\ge0$
(b) to D, Range of $f=\sqrt {x-3}$ is $[0,\infty)$
(c) to C, Domain of $f=x^2-3$ is $(-\infty,\infty)$
(d) to B, Range of $f=x^2+3$ is $[3,\infty)$
(e) to C, Domain of $f=\sqrt[3] {x-3}$ is $(-\infty,\infty)$
(f) to C, Range of $f=\sqrt[3] x+3$ is $(-\infty,\infty)$
(g) to C, Domain of $f=|x|-3$ is $(-\infty,\infty)$
(h) to D, Range of $f=|x+3|$ is $[0,\infty)$
(i) to D, Domain of $x=y^2$ is $[0,\infty)$
(j) to C, Range of $x=y^2$ is $(-\infty,\infty)$