Answer:Option a[tex]f(x) = e^{x-1} -2[/tex]Step-by-step explanation:If the graph of the function [tex]y=f(x+h) +b[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]b> 0[/tex] the graph moves vertically upwards b units.
If [tex]b <0[/tex] the graph moves vertically down b unitsIf [tex]h<0[/tex] The graph moves horizontally h units to the rightIf [tex]h>0[/tex] The graph moves horizontally h units to the leftIn this problem we have the parent function [tex]y=e^x[/tex] We know that the parent function is translated 1 unit rigth and 2 units down. This is:[tex]h<0 = -1\\\\b < 0 = -2[/tex]Finally the transformation is: [tex]y=f(x-1) -2[/tex][tex]f(x) = e^{x-1} -2[/tex]