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