Question

begin by graphing f(x) = \log_2 x. then use transformations of this graph to graph the given function. what is the vertical asymptote? use the graphs to determine the given function’s domain and range.\
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\quad g(x) = \log_2(x + 5)\
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\bigcirc d. the graph of f(x) = \log_2 x should be shifted 5 units upward.\
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graph the function g(x) = \log_2(x + 5). graph the asymptote of g(x) as a dashed line. use the graphing tool to graph the equations.\
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what is the vertical asymptote of g(x)?\
\quad x = -5\
(type an equation.)\
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what is the domain of g(x) = \log_2(x + 5)?\
( simplify your answer. type your answer in interval notation )

Explanation:

Step1: Recall Domain of Log Function

For a logarithmic function \( \log_b(u) \), the argument \( u > 0 \). For \( g(x)=\log_2(x + 5) \), set \( x + 5>0 \).

Step2: Solve Inequality

Solve \( x + 5>0 \) by subtracting 5 from both sides: \( x>-5 \).

Step3: Write in Interval Notation

The domain in interval notation is \( (-5, \infty) \).

Answer:

\((-5, \infty)\)