Answer
Domain: (0, ∞)
Range: (-∞, ∞)
Asymptote: x = 0
See graph below.
Work Step by Step
This problem just asks for the graph of the function, domain, range, and asymptote.
Given $f(x) = -\log_{2} (x) + 2 $
The graph in black represents $\log_{2} (x) $
The function (in red) is a reflection about the x-axis, then a shift up 2 units
Domain: (0, ∞)
Range: (-∞, ∞)
Asymptote: x = 0