In doing multiple transformations in exponential functions, which is done first, the horizontal shift or reflection in x-or y-axis?
It does not matter which is done first. In the following graph of the exponential (in black), a horizontal shift of 2 right (in red) then reflected across x-axis (green).
Now, I'll start with y = 2^x (in black), then reflect across x-axis (red), then shift 2 right (in green.)
As you see, the final "green" graph is the same in both situations, resulting in the fact that it does not matter which transformation is done first.
How about the order in this one. f(x) = 2^x. Describe the transformation that yields g(x) = 2^(-x+3). Thank you.