use the given function f to answer parts (a) through (f) below. f(x)=4 + ln x (c) from the graph, determine…

use the given function f to answer parts (a) through (f) below. f(x)=4 + ln x (c) from the graph, determine the range and any asymptotes of f. the range of f is (-∞,∞) (type your answer in interval notation.) determine the vertical asymptote of f. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the vertical asymptote of f is x = (simplify your answer.) b. there is no vertical asymptote.

use the given function f to answer parts (a) through (f) below. f(x)=4 + ln x (c) from the graph, determine the range and any asymptotes of f. the range of f is (-∞,∞) (type your answer in interval notation.) determine the vertical asymptote of f. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the vertical asymptote of f is x = (simplify your answer.) b. there is no vertical asymptote.

Answer

Explanation:

Step1: Recall the properties of the natural - log function

The function is (y = 4+\ln x). The domain of (y = \ln x) is ((0,\infty)).

Step2: Analyze the vertical asymptote

As (x\to0^{+}), (\ln x\to-\infty). For the function (y = 4+\ln x), the vertical asymptote occurs when the argument of the natural - log function approaches 0. So the vertical asymptote is (x = 0).

Answer:

A. The vertical asymptote of (f) is (x = 0)