Answer: k = -3
Step-by-step explanation:
If we have a function f(x) defined in the real numbers we can transform it by moving it vertically doing [tex]y = f (x) + k[/tex]
If k is greater than zero the graph of f(x) will move k units up. If k is less than zero the graph of f(x) will move k units down.
In the same way if you make the transformation [tex]y = f (x + h)[/tex] then the graph of f(x) will move h units to the right if [tex]h <0[/tex] and move h units to the left if [tex]h> 0[/tex].
In this problem we have to:
[tex]f(x) =(\frac{1}{3})^x[/tex]
then we see that the graph of g(x) is displaced 3 units down. This means that [tex]k = -3[/tex]
Also the graph of g(x) is equal to the graph of f(x) displaced 5 units to the right so that [tex]h = -5[/tex]
