summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y =…

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x).\n\nf(x) = ln(x + 5) - 4\n\na. the x - intercept(s) of f is x = e^{4}-5\n(type an exact answer. use a comma to separate answers as needed.)\nb. the function f has no x - intercepts.\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. the y - intercept of f is y = ln(5)-4\n(type an exact answer. use a comma to separate answers as needed.)\nb. the function f has no y - intercept.\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. the function f is increasing on the subinterval(s)\n(type your answer in interval notation. use a comma to separate answers as needed.)\nb. the function f is never increasing.

summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x).\n\nf(x) = ln(x + 5) - 4\n\na. the x - intercept(s) of f is x = e^{4}-5\n(type an exact answer. use a comma to separate answers as needed.)\nb. the function f has no x - intercepts.\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. the y - intercept of f is y = ln(5)-4\n(type an exact answer. use a comma to separate answers as needed.)\nb. the function f has no y - intercept.\n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\n\na. the function f is increasing on the subinterval(s)\n(type your answer in interval notation. use a comma to separate answers as needed.)\nb. the function f is never increasing.

Answer

Explanation:

Step1: Find the domain

For (y = \ln(x + 5)-4), the argument of the logarithm must be positive. So (x+5>0), which gives (x>- 5). The domain is ((-5,\infty)).

Step2: Analyze the derivative

The derivative of (y=f(x)=\ln(x + 5)-4) is (y^\prime=\frac{1}{x + 5}). Since (x>-5), then (y^\prime=\frac{1}{x + 5}>0) for all (x\in(-5,\infty)).

Answer:

A. The function (f) is increasing on the sub - interval ((-5,\infty))