Question

Pls help me ask this quickly

Answer 1

The graph is shown in the picture attached.

range: (-∞, ∞)

domain: (2, ∞)

Explanation:

To graph g(x) follow the next steps:

1. Graph
   `log_4(x)`. It passes through (1,0) and (4,1) and has the form of logarithmic functions
2. 
   `log_4(x-2)` has the graph of
   `log_4(x)` translated 2 units to the right, then it passes through (3,0) and (6,1)
3. 
   `g(x) = 3 + log_4(x-2)` has the graph of
   `log_4(x-2)` 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
`log_4(x)` is all real numbers greater than zero, then the domain of
`log_4(x-2)` is all real numbers greater than two.