Question

question 17, 4.2.53 - setup & solve
part 3 of 5
points: 0 of 1
begin by graphing f(x) = log₂x. 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.

g(x) = log₂(x + 5)

determine the transformations that are needed to go from f(x) = log₂x to
the given graph. choose the correct answer below.
a. the graph of f(x) = log₂x should be shifted 5 units to the left.
b. the graph of f(x) = log₂x should be shifted 5 units downward.
c. the graph of f(x) = log₂x should be shifted 5 units to the right.
d. the graph of f(x) = log₂x should be shifted 5 units upward.

graph the function g(x) = log₂(x + 5). graph the asymptote of g(x) as a
dashed line. use the graphing tool to graph the equations.

what is the vertical asymptote of g(x)?
(type an equation.)

Explanation:

Step1: Recall Vertical Asymptote of Log Function

For a logarithmic function \( f(x)=\log_b(x - h) \), the vertical asymptote is \( x = h \) (where the argument \( x - h = 0 \)).

Step2: Analyze \( g(x)=\log_2(x + 5) \)

Rewrite \( g(x)=\log_2(x - (-5)) \). Comparing with \( \log_b(x - h) \), we have \( h=-5 \). So the vertical asymptote occurs when \( x + 5 = 0 \), which gives \( x=-5 \).

Answer:

The vertical asymptote of \( g(x)=\log_2(x + 5) \) is \( \boldsymbol{x = -5} \).