Answer:
See the graph and explanation below.
Step-by-step explanation:
For this case we have the following function:
[tex] f(x) = ln(x-5)[/tex]
The domain for this function is given by:
[tex] x-5 >0[/tex] since the natural log is not defined for negative numbers
[tex] x>5[/tex] , [tex] D = x \in (5,\infty)[/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 =5.5, 6,7,8,9,10[/tex] and we can calculate the values for f(x) like this
x=5.5
[tex] f(x=5.5) = ln(5.5-5) = ln(0.5) =-0.693[/tex]
x=6
[tex] f(x=6) = ln(6-5) = ln(1) =0[/tex]
That represent the x intercept
x=7
[tex] f(x=7) = ln(7-5) = ln(2) =0.693[/tex]
x=8
[tex] f(x=8) = ln(8-5) = ln(3) =1.099[/tex]
x=9
[tex] f(x=6) = ln(9-5) = ln(4) =1.386[/tex]
x=10
[tex] f(x=10) = ln(10-5) = ln(5) =1.609[/tex]
And that represent the x intercept
And then we can see the plot on the figure attached.
