1. If point $P(x, y)$ moves on the line $x+3 y=3$, then the minimum value of the function $f(x, y)=3^{x}+9^{y}$ is equal to ( ).
(A) $5\left(\frac{27}{4}\right)^{\frac{1}{5}}$
(B) $7\left(\frac{27}{9}\right)^{\frac{1}{7}}$
(C) $7\left(\frac{16}{9}\right)^{\frac{1}{7}}$
(D) $3\left(\frac{5}{2}\right)^{\frac{1}{3}}$
-1. A.
$$
\begin{array}{l}
f(x)=3^{x}+9^{y}=3^{x}+9^{\frac{3-x}{3}} \\
=3^{x}+3^{2\left(1-\frac{x}{3}\right)}=3^{x}+3^{2-\frac{2}{3} x} \\
=\frac{1}{2} \cdot 3^{x}+\frac{1}{2} \cdot 3^{x}+3^{1-\frac{2}{3} x}+3^{1-\frac{2}{3} x}+3^{1-\frac{2}{3} x} \\
\geqslant 5 \cdot \sqrt[5]{\frac{1}{2} \cdot 3^{x} \cdot \frac{1}{2} \cdot 3^{x} \cdot 3^{1-\frac{2}{3} x} \cdot 3^{1-\frac{2}{3} x} \cdot 3^{1-\frac{2}{3} x}} \\
=5 \cdot \sqrt[5]{\frac{1}{4} \cdot 3^{3}}=5\left(\frac{27}{4}\right)^{\frac{1}{5}},
\end{array}
$$

When and only when $\frac{1}{2} \cdot 3^{x}=3^{1-\frac{2}{3} x}$, i.e., $x=\frac{3}{5}\left(1+\log _{3} 2\right)$, the equality holds.
Therefore, the minimum value of $f(x, y)$ is $5\left(\frac{27}{4}\right)^{\frac{1}{5}}$.