You can do the graphing....
You need to determine what the sequence of transformations does to each "vertex" of the graph.
You first need to rewrite the transformation so that the expression in parentheses is of the form (x-a):
--> 
In that form, you can see the sequence of transformations is
(1) (x-3) --> horizontal shift of 3
(2) -(x-3) --> reflect in y-axis
(3) -2f(-(x-3)) --> vertical stretch by -2 (reflect in x-axis and double)
(4) -2f(-(x-3))+4 --> vertical shift of 4
Now perform that sequence of transformations to each given point to find the image under the given transformation.
A B C D E F
(0) (-1,3) (2,0) (3,-3) (4,2) (6,1) (8,-2)
(1) (2,3) (5,0) (6,-3) (7,2) (9,1) (11,-2)
(2) (-2,3) (-5,0) (-6,-3) (-7,2) (-9,1) (-11,-2)
(3) (-2,-6) (-5,0) (-6,6) (-7,-4) (-9,-2) (-11,4)
(4) (-2,-2) (-5,4) (-6,10) (-7,0) (-9,2) (-11,8)
Those are the coordinates of the images of the original points under the given transformation.
