Question 1142094
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You can do the graphing....<br>
You need to determine what the sequence of transformations does to each "vertex" of the graph.<br>
You first need to rewrite the transformation so that the expression in parentheses is of the form (x-a):<br>
{{{y = -2f(-x+3)+4}}}  -->  {{{y = -2f(-(x-3))+4}}}<br>
In that form, you can see the sequence of transformations is<br>
(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<br>
Now perform that sequence of transformations to each given point to find the image under the given transformation.<br><pre>

        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)<br></pre>
Those are the coordinates of the images of the original points under the given transformation.