The point (1, 1) is on f(x). after a series of 3 transformations, (1, 1) ha been moved to (2, -7). write a function g(x) that represents the transformations on f(x)

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