Option B: [tex]y=4^{(x-6)}[/tex] is the equation of the new graph.
Explanation:
Given that the equation of the graph is [tex]y=4^x[/tex]
We need to determine the new equation of the graph.
Equation of the graph:
Given that the graph [tex]y=4^x[/tex] is shifted 6 units to the right.
The new equation of the graph can be determined using the rule,
[tex]f(x)=f(x-h)[/tex]
if the graph is shifted h units to the right.
Thus, the new equation of the graph that is shifted 6 units to the right can be written using the rule is given by
[tex]y=4^{(x-6)}[/tex]
Hence, the new equation of the graph is [tex]y=4^{(x-6)}[/tex]
Therefore, Option B is the correct answer.
