In doing multiple transformations in exponential functions, which is done first, the horizontal shift or reflection in x or y axis?

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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,...

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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.

 

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