Answer
Domain: (-∞, -1) U (-1, ∞)
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 $r(x) = \frac{3}{x+1}$
From $\frac{1}{x}$, the graph is transformed one unit to the left and stretched by a factor of 3 vertically
The vertical asymptote is at x= -1, so the domain is (-∞, -1) U (-1, ∞)
The horizontal asymptote is at y = 0, so the range is (-∞, 0) U (0, ∞)
Blue graph is $\frac {1}{x}$
Green graph is $r(x) = \frac{3}{x+1}$
