Find the range of the function f(x)=sin2(x)+3sin(x)cos(x)f(x) = \sin^2(x) + \sqrt{3}\sin(x)\cos(x)f(x)=sin2(x)+3sin(x)cos(x).
[0,1][0, 1][0,1]
[1−32,1+32][\frac{1-\sqrt{3}}{2}, \frac{1+\sqrt{3}}{2}][21−3,21+3]
[1−3,1+3][1-\sqrt{3}, 1+\sqrt{3}][1−3,1+3]
[12−1,12+1][\frac{1}{2}-1, \frac{1}{2}+1][21−1,21+1]