You're on the right track, but you're having trouble with the endpoints.
The points $(-3, -2)$ and $(4, -2)$ are on the graph in a), which means that your domain should actually be $x \in [-3, 4]$ in interval notation to indicate that $x = -3$ and $x = 4$ are included. This would be reflected in the set-builder notation by using inequalities with "or equal to", so that you'd have $\{x \in \Bbb R \mid -3 \le x \le 4\}$.
For part c), you're again almost right, except for the endpoints. Their $x$- and $y$-coordinates need to be included, so you'd need brackets for interval notation, and all $\le$'s for the set-builder notation. So, for the range, I would write $\{y \in \Bbb R \mid -3 \le y \le 3\}$, using $y$ rather than $x$.
Now, in addition to filled-in circles, some graphs have arrows. These indicate that the graph "keeps going" in (roughly) whatever direction the arrows point. In b), this would be reflected as an interval $x \in (-\infty, 3]$ for the domain.
Notice for b) that $x$ needs to only be "at most $3$" (not "at least" anything), and thus you'll only need a single inequality, rather than the compound ones you would use on graphs that have a definite starting and ending point.
I'll let you give the rest a shot; most of what you had was spot-on.
a) You are correct.
b) The tiding is coming in, since the height of it is rising as time goes on.
c) The domain should include $0$ and the range should be $\{y \: \:|\:5 \le y \le 30, y \in \mathbb{R} \} $
Best Answer
ignoramus was right; your only mistake was not using square brackets in the domain of the first graph. The domain and range of a graph are nothing more than all the $x$- and $y$-values, respectively, that the graph includes, so everything else is correct.