Question

Graphing Logarithmic Expressions In Exercise, sketch the graph of the function.
y = In(4 - x)

Answer 1

See the graph and explanation below.

Explanation:

For this case we have the following function:

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

The domain for this function is given by:

`4-x >0` since the natural log is not defined for negative numbers

`x<4` ,
`D = x \in (-\infty ,4)`

We can calculate some points in order to see the tendency of the graph, we can select a set of points for example
`x =-3,-2,-1,0,1,2,3,4` and we can calculate the values for f(x) like this

x=-3

`f(x=-3) = ln(4+3) = ln(7) =1.946`

x=-2

`f(x=-2) = ln(4+2) = ln(6) =1.792`

x=-1

`f(x=-1) = ln(4+1) = ln(5) =1.609`

x=0

`f(x=0) = ln(4-0) = ln(4) =1.386`

This point correspond to the y intercept.

x=1

`f(x=1) = ln(4-1) = ln(3) =1.099`

x=2

`f(x=2) = ln(4-2) = ln(2) =0.693`

x=3

`f(x=3) = ln(4-3) = ln(1) =0`

And that represent the x intercept

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