3. If the function $f(x, y)=\sqrt{x^{2}+y^{2}-6 y+9}+\sqrt{x^{2}+y^{2}+2 \sqrt{3} x+3}+\sqrt{x^{2}+y^{2}-2 \sqrt{3} x+3}$, then the minimum value of $f(x, y)$ is
A. $2 \sqrt{3}+3$
B. $2 \sqrt{3}+2$
C. 6
D. 8
$f(x, y)=\sqrt{x^{2}+(y-3)^{2}}+\sqrt{(x+\sqrt{3})^{2}+y^{2}}+\sqrt{(x-\sqrt{3})^{2}+y^{2}}$, According to the knowledge related to Fermat's point, when $x=0, y=1$, $f(x, y)$ reaches its minimum value of 6. Therefore, the answer is $C$.