Which of the following describes the transformations of g (x) = negative (2) superscript x + 4 baseline minus 2 from the parent function f (x) = 2 superscript x?
shift 4 units left, reflect over the x-axis, shift 2 units down
shift 4 units left, reflect over the y-axis, shift 2 units down
shift 4 units right, reflect over the x-axis, shift 2 units down
shift 4 units right, reflect over the y-axis, shift 2 units down

First option.

Step-by-step explanation:

Below are some transformations for a function :

1. If , the function is shifted "k" units up.

2 If , the function is shifted "k" units down.

3. If , the function is shifted "k" units right.

4. If , the function is shifted "k" units left.

5. If , the function is reflected over the x-axis.

6. If , the function is reflected over the y-axis.

Then, given the parent function :

And knowing that the the other function is:

You can identify that the function is obtained by:

- Shifting the function 4 units left.

-  Reflecting the function   4 over the x-axis.

- Shifting the function 2 units down.

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.