Question

In Exercise, sketch the graph of the function. f(x) = ln(x – 5)

Answer 1

Answer:

See the graph and explanation below.

Step-by-step explanation:

For this case we have the following function:

$f(x) = ln(x-5)$

The domain for this function is given by:

$x-5 >0$ since the natural log is not defined for negative numbers

$x>5$ , $D = x \in (5,\infty)$

We can calculate some points in order to see the tendency of the graph, we can select a set of points for example $x =5.5, 6,7,8,9,10$ and we can calculate the values for f(x) like this

x=5.5

$f(x=5.5) = ln(5.5-5) = ln(0.5) =-0.693$

x=6

$f(x=6) = ln(6-5) = ln(1) =0$

That represent the x intercept

x=7

$f(x=7) = ln(7-5) = ln(2) =0.693$

x=8

$f(x=8) = ln(8-5) = ln(3) =1.099$

x=9

$f(x=6) = ln(9-5) = ln(4) =1.386$

x=10

$f(x=10) = ln(10-5) = ln(5) =1.609$

And that represent the x intercept

And then we can see the plot on the figure attached.