The graph of the function:
[tex]g(x)=ln(4-x)[/tex]
Can be obtained by using the parent function:
[tex]f(x)=ln(x)[/tex]
Whose graph is shown below:
We must first turn x into -x by making a reflection over the y-axis. This way, the function becomes:
[tex]f(-x)=ln(-x)[/tex]
And the graph is:
Finally, we just add 4 to x to translate the graph 4 units to the right to get our desired function:
[tex]g(x)=f(4-x)=ln(4-x)[/tex]
The graph is shifted 4 units to the right as shown:
