Transformation of Exponential Functions Rule

Please explain how to transform exponential functions

To graph function y=3^(x-1) we shift function y=3^x one unit to the right ( the opposite of -1). I understand this far. Now to graph y=3^(1-x) which is the same as y=3^(-x+1), we need to shift the graph of y=3^-x one unit to the right. My question is why to the right when the opposite of 1 is -1, why not to the left. The texbook does not explain, when I plug in the numbers in y=3^(-x+1) x=0, y=3, the shift should be to the right, but what is the rule?

Thank you