QUESTION IMAGE
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\.
Determine the domain and range of the function
Find the x-intercept of the function
Identify the horizontal and vertical shifts
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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