Given: The function below:
[tex]f(x)=2\log _2(x-2)[/tex]
The function f(x) is logarithmic function with a vertical asymptote
[tex]\begin{gathered} x-2=0 \\ x=2 \end{gathered}[/tex]
Calculate the domain
From the graph shown the domain is
[tex]\begin{gathered} x>2 \\ (2,\infty) \end{gathered}[/tex]
From the graph, the range is
[tex]\begin{gathered} -\infty
HenceThe function f(x) is logarithmic function with a vertical asymptote of 2. The range of the function is (- ∞, ∞) and it is increasing on its domain of (2, ∞)
