[tex]\begin{gathered} f(x)=(\frac{1}{4})^x \\ \end{gathered}[/tex]
Let's find the y-intercept:
[tex]\begin{gathered} x=0 \\ f(0)=(\frac{1}{4})^0 \\ f(0)=1 \end{gathered}[/tex]
As we can see the parent function crosses the y-axis at (0,1), since the new graph crosses the y-axis at (0,-2), then:
[tex]\begin{gathered} 1-b=-2 \\ b=3 \end{gathered}[/tex]
Therefore, we need to translate the function f(x) 3 units down in order to get g(x), so:
[tex]g(x)=(\frac{1}{4})^x-3[/tex]
