Notice that the function is of the form g(x)=4^(ax- h), where a= 0.5, or 1 2, and h= 5. Therefore, the graph of g is a translation 5 units to the right, followed by a horizontal stretch by a factor of 2 of the graph of its parent function. Let's show the transformations one at a time.
Translation
We will first consider the function y=4^(x-5). This is a horizontal translation of f(x)=4^x to the right by 5 units.
Horizontal Stretch
Be aware that 0.5= 12. Therefore, if in y=4^(x-5) we multiply the x-variable by 0.5, we obtain a horizontal stretch by a factor of 2. The resulting function is g(x)=4^(0.5x-5).
Extra
Possible Transformations
The following table illustrates the general form for all possible transformations of functions.
