Answer
Domain: (-∞, -2) U (-2, ∞)
Range: (-∞, 3) U (3, ∞)
See graph below
Work Step by Step
The question asks for a graph of the function and the function's domain and range.
Given $r(x) = \frac{3x-3}{x+2}$
By dividing the function, $r(x) = 3 - \frac{9}{x+2}$
From $\frac{1}{x}$, the graph is transformed two units to the left, stretched vertically by a factor of 9, reflected about the x-axis, then shifted up three units
The vertical asymptote is at x= -2, so the domain is (-∞, -2) U (-2, ∞)
The horizontal asymptote is at y = 3, so the range is (-∞, 3) U (3, ∞)
Blue graph is $\frac {1}{x}$
Green graph is $r(x) = \frac{3x-3}{x+2}$
