Looking at the graph of g(x) (the red graph), we can see that it has the same format of f(x), but it is 9 units above it (f(x) passes through (0, -6) and g(x) passes through (0, 3)).
Therefore the graph of g(x) can be created using a translation of 9 units up from the graph of f(x).
That means we can write the following expression:
[tex]\begin{gathered} g(x)=f(x)+9\\ \\ g(x)=\frac{1}{4}3^x-6+9\\ \\ g(x)=\frac{1}{4}3^x+3 \end{gathered}[/tex]
So the correct option is B.
