Answer:
The graph is shown in the picture attached.
range: (-∞, ∞)
domain: (2, ∞)
Step-by-step explanation:
To graph g(x) follow the next steps:
- Graph [tex]log_4(x)[/tex]. It passes through (1,0) and (4,1) and has the form of logarithmic functions
- [tex]log_4(x-2)[/tex] has the graph of [tex]log_4(x)[/tex] translated 2 units to the right, then it passes through (3,0) and (6,1)
- [tex]g(x) = 3 + log_4(x-2)[/tex] has the graph of [tex]log_4(x-2)[/tex] translated 3 units up, then it passes through (3,3) and (6,4)
The range of a logarithmic function is all real numbers.
The domain is of [tex]log_4(x)[/tex] is all real numbers greater than zero, then the domain of [tex]log_4(x-2)[/tex] is all real numbers greater than two.
