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use the given logarithmic function to answer the following questions. \…

Question

use the given logarithmic function to answer the following questions.

\\f(x) = \ln(x - 3) - 3\\

a) what are the domain and range of \\(f\\)?

b) what is the \\(x\\)-intercept of the graph of \\(f\\)? enter your answer as an ordered pair. if no \\(x\\)-intercept exists, enter none.

c) the graph of \\(\ln(x)\\) is shown below. sketch the graph of \\(f(x) = \ln(x - 3) - 3\\) by entering values for the horizontal/vertical shift(s) in the boxes below, then clicking \graph\.

Explanation:

Determine the domain and range of the function

$$ LATEXBLOCK0 $$

Find the x-intercept of the function

$$ LATEXBLOCK1 $$

Identify the horizontal and vertical shifts

$$ LATEXBLOCK2 $$

Answer:

Question a

Domain: <blank>\((3, \infty)\)</blank>
Range: <blank>\((-\infty, \infty)\)</blank>

Question b

\(x\)-intercept: <blank>\((e^3 + 3, 0)\)</blank>

Question c

Horizontal shift: <blank>3</blank> units to the right
Vertical shift: <blank>3</blank> units down