Answer: Option C
[tex]g(x) = 4 ^ x-1[/tex]
Step-by-step explanation:
If we have a function f(x) and we want to move its graph vertically then we apply the transformation:
[tex]g (x) = f (x) + k.[/tex]
So:
If [tex]k> 0[/tex] the function g(x) will be the function f(x) displaced k units up
If [tex]k <0[/tex] the function g(x) will be the function f(x) displaced k units down.
In this case we know that the graph of f(x) moves 5 units up.
then [tex]k> 0[/tex] and [tex]k = 5[/tex]
Therefore [tex]g (x) = f(x) +5[/tex]
[tex]g(x) = 4 ^ x - 6 +5\\\\g(x) = 4 ^ x-1[/tex]
