2. As shown in Figure 8-3, a certain type of bacteria divides every two hours (each bacterium splits into two, and the time for division is negligible). At the start of the study, there are two bacteria, which continue to divide throughout the study. The total number of bacteria $y$ is a function of the time $t$ of the study, denoted as $y=f(t)$.
(1) Write the domain and range of the function $y=f(t)$;
(2) In the given coordinate system, draw the graph of $y=f(t)$ $(0 \leqslant t \leqslant 6)$;
(3) Write the total number of bacteria at the $n$-th hour of the study $(n \geqslant 0$, $n \in \mathbf{Z}$) in terms of $n$.
2. (1) Domain $[0,+\infty)$, Range $\left\{y \mid y=2^{n}, n \in \mathbf{N}_{+}\right\}$;
(2) Graph omitted;
(3) When $n$ is even, $y=2^{\frac{n}{2}+1} ;$ when $n$ is odd, $y=2^{\frac{n+1}{2}}$.