Answer
Domain: (-∞, 2) U (2, ∞)
Range: (-∞, 0) U (0, ∞)
See graph below
Work Step by Step
The question asks for a graph of the function and the function's domain and range.
Given $r(x) = \frac{-2}{x-2}$
From $\frac{1}{x}$, the graph is transformed two units to the right, stretched by a factor of 2 vertically, then reflected about the x-axis
The vertical asymptote is at x= 2, so the domain is (-∞, 2) U (2, ∞)
The horizontal asymptote is at y = 0, so the range is (-∞, 0) U (0, ∞)
Blue graph is $\frac {1}{x}$
Green graph is $r(x) = \frac{-2}{x-2}$
