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.
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.
Best Answer
If you're given a graph the range is all of the $y$ values and the domain is all of the $x$ values where the graph exists.
For example, consider this graph
What are the $x$ values at which the function is defined? Well we can see it starts at $-3$ on the left and keeps going until $4$. Notice, that even though this is a piecewise function, every single $x$ between $-3$ and $4$ corresponds to a point on the graph. Then we just need to take into a account whether the endpoints are included or not. In this case $-3$ is but $4$ is not. So the domain, in set builder notation, is $\{x\mid -3\le x\lt 4\}$.
As for the range, we look at the $y$ values. The lowest $y$ value at which the function is defined is $-3$. Then continuing up we see a break from $0$ to $1$. There is no point on the graph that corresponds to $y$ values between those two numbers. But then it continues at $1$ and goes up to $2$. In this case $-3$, $0$, and $1$ are definitely included. It might be slightly harder to tell that $2$is included, but it is. So the range is $\{y \mid -3\le y\le 0 \text{ or } 1\le y \le 2\}$.