\[ m(x)=-2 \sqrt{x-2}+1 \] Step 1 of 2: Graph the original function by indicating how the more basic function has been shifted, reflected, stretched, or compressed. Answer Tables Keypad Keyboard Shortcuts Select the type of transformations to create the correct graph. Any further inputs required to complete the transformations will appear when the appropriate selection is made. Horizontal Shift C Left Right None Vertical Stretch/Compress Stretch Compress None $x$-Axis Reflection Yes No Enable Zoom/Pan

Step 1 ：The basic function here is the square root function, \(y = \sqrt{x}\). The given function is \(m(x)=-2 \sqrt{x-2}+1\).

Step 2 ：From the given function, we can observe that the function is multiplied by -2, which is a vertical stretch by a factor of 2 and a reflection in the x-axis.

Step 3 ：The function is shifted 2 units to the right, which is a horizontal shift.

Step 4 ：The function is shifted 1 unit up, which is a vertical shift.

Step 5 ：So, the transformations applied to the basic function are: a vertical stretch by a factor of 2, a reflection in the x-axis, a horizontal shift of 2 units to the right, and a vertical shift of 1 unit up.

Step 6 ：\(\boxed{\text{The transformations applied to the basic function are: a vertical stretch by a factor of 2, a reflection in the x-axis, a horizontal shift of 2 units to the right, and a vertical shift of 1 unit up.}}\)