Question

What are the features of the function f(2) = 2 log, (2 -2) graphed below?

Answer 1

Given: The function below:

$f(x)=2\log _2(x-2)$

The function f(x) is logarithmic function with a vertical asymptote

$\begin{gathered} x-2=0 \\ x=2 \end{gathered}$

Calculate the domain

From the graph shown the domain is

$\begin{gathered} x>2 \\ (2,\infty) \end{gathered}$

From the graph, the range is

[tex]\begin{gathered} -\inftyHence

The 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, ∞)