Transformations of functions are simply moving the graph around the plot in the Cartesion plane. It can be done through translations, reflections and rotations. For this problem, 3 transformations occurred from point (1,1) to (2,-7). I think that would be two translations and 1 rotation.
Translation is when you move the point of the graph either horizontally or vertically. The first translation is moving x=1 coordinate to x=2 coordinate by translating 1 unit to the right. Next, you move y = 1 coordinate to y = 7 by translating 6 units up. The resulting point after these two translations is (2,7). The last transformation is rotation of 270° clockwise about the origin. There are already rules for rotations of 90, 180, and 270°. The rule for a 270-degree clockwise rotation is point (a,b) becomes point (a,-b). Therefore, after rotation, the final point would be located at point (2,-7).
In summary, the transformations involved were:
* translation 1 unit to the right
* translation 6 units up
* 270-degree clockwise rotation