Question

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of ( y = f(x) ).
( f(x)=ln (x + 5)-4 )
a. the domain of ( f ) is ( (-5, infty) ).
(type your answer in interval notation. use a comma to separate answers as needed.)
b. the domain of ( f ) is empty.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the ( x )-intercept(s) of ( f ) is ( x = e^{4}-5 ).
(type an exact answer. use a comma to separate answers as needed.)
b. the function ( f ) has no ( x )-intercepts.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the ( y )-intercept of ( f ) is ( y = )
(type an exact answer. use a comma to separate answers as needed.)
b. the function ( f ) has no ( y )-intercept.

Explanation:

Step1: Find the y - intercept

The y - intercept occurs when \(x = 0\).
Substitute \(x=0\) into \(y = f(x)=\ln(x + 5)-4\).
We get \(y=\ln(0 + 5)-4=\ln(5)-4\).

Answer:

A. The y - intercept of \(f\) is \(y=\ln(5)-4\)