Answer:
The correct option is B.
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{1}{4}3^x-6[/tex]
From the given graph it is clear that the graph of f(x) shifts approximately 8 units up. It means the transformation is defined as
[tex]g(x)=f(x)+b[/tex]
Where b is vertical shift of the function.
If b>0, then graph of f(x) shifts b units up and if b<0, then graph of f(x) shifts b units down.
The value of b is 8.
[tex]g(x)=f(x)+8[/tex]
[tex]g(x)=\frac{1}{4}3^x-6+8[/tex]
[tex]g(x)=\frac{1}{4}3^x+2[/tex]
Therefore the correct option is B.
