begin by graphing f(x)=log₂x. then use transformations of this graph to graph the given function. what is…

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 functions domain and range.\ng(x)=log₂(x + 4)\nwhat is the domain of g(x)=log₂(x + 4)?\n(simplify your answer. type your answer in interval notation.)

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 functions domain and range.\ng(x)=log₂(x + 4)\nwhat is the domain of g(x)=log₂(x + 4)?\n(simplify your answer. type your answer in interval notation.)

Answer

Explanation:

Step1: Recall domain of logarithmic function

The domain of $y = \log_a(u)$ is $u>0$. For $g(x)=\log_2(x + 4)$, we set $u=x + 4$.

Step2: Solve the inequality

Set $x+4>0$. Subtract 4 from both sides of the inequality: $x+4-4>0 - 4$. So $x>-4$.

Answer:

$(-4,\infty)$