Question

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)

Answer 1

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

Answer 2

Answer:

Step-by-step explanation:

Given that the point (1,1) is on f(x).

Three series of tranformations have been done to get the new point (2,-7)

Note that the three transformations need not be unique.

We can do the transformations in the following order

i) (1,1) is reflected about x axis.  So new point would be (1,-1)

ii) Shift the curve horizontally to the right by 1 unit.  Now new point transformed is (2,-1)

iii) Now shift vertically down by 6 units so that we reach (2,-7)

Thus the above transformations are one of the possibilities.