Question

Hello! Having a little trouble on this question, thanks for your help!

Answer 1

The graph of the function:

`g(x)=ln(4-x)`

Can be obtained by using the parent function:

`f(x)=ln(x)`

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:

`f(-x)=ln(-x)`

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:

`g(x)=f(4-x)=ln(4-x)`

The graph is shifted 4 units to the right as shown: