ans

024730
$\pm 2\pi$

024731
$(0,2]$

024732
$[-\dfrac{\pi}{4}+k\pi, \dfrac{\pi}{4}+k\pi]$, $k\in \mathbf{Z}$

024733
奇

024734
$\dfrac{5\pi}{6}$或$\dfrac{11\pi}{6}$

024735
$\{x|\dfrac{\pi}{3}+2k\pi<x<\dfrac{2\pi}{3}+2k\pi, \ k\in \mathbf{Z}\}$

024736
$\{9\}\cup [18,+\infty)$

024737
$3^{x-4}$

024738
\begin{tikzpicture}[>=latex, scale = 0.5]
\draw [->] (-2,0) -- (8,0) node [below] {$x$};
\draw [->] (0,-3) -- (0,5) node [left] {$y$};
\draw (0,0) node [below left] {$O$};
\draw [domain = -2:8, samples = 200] plot (\x,{3*sin(\x/pi*180+30)+1});
\draw [dashed] (pi/3,0) --++ (0,4) -- (0,4) (4*pi/3,0) --++ (0,-2) -- (0,-2);
\draw (pi/3,0) node [below] {$\frac{\pi}{3}$} (0,4) node [left] {$4$} (4*pi/3,0) node [above] {$\frac{4\pi}{3}$} (0,-2) node [left] {$-2$};
\end{tikzpicture}