Answer:
See the graph and explanation below.
Step-by-step explanation:
For this case we have the following function:
[tex] f(x) = ln(4-x)[/tex]
The domain for this function is given by:
[tex] 4-x >0[/tex] since the natural log is not defined for negative numbers
[tex] x<4[/tex] , [tex] D = x \in (-\infty ,4)[/tex]
We can calculate some points in order to see the tendency of the graph, we can select a set of points for example [tex] x =-3,-2,-1,0,1,2,3,4[/tex] and we can calculate the values for f(x) like this
x=-3
[tex] f(x=-3) = ln(4+3) = ln(7) =1.946[/tex]
x=-2
[tex] f(x=-2) = ln(4+2) = ln(6) =1.792[/tex]
x=-1
[tex] f(x=-1) = ln(4+1) = ln(5) =1.609[/tex]
x=0
[tex] f(x=0) = ln(4-0) = ln(4) =1.386[/tex]
This point correspond to the y intercept.
x=1
[tex] f(x=1) = ln(4-1) = ln(3) =1.099[/tex]
x=2
[tex] f(x=2) = ln(4-2) = ln(2) =0.693[/tex]
x=3
[tex] f(x=3) = ln(4-3) = ln(1) =0[/tex]
And that represent the x intercept
And then we can see the plot on the figure attached.
