Question

how do I write a function that describes the given transformation

Answer 1

1) Considering that this is our parent function:

$f(x)=2^x$

2) Then let's visualize what happens when we transform it to :

$g(x)=2^{x-3}+1$

3) So now let's reflect that across the y-axis, and vertically shrink that by 1/3: