Answer
Domain: (-∞, -4) U (4, ∞)
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 $r(x) = \frac{1}{x+4}$
From $\frac{1}{x}$, the graph is transformed four units to the left
The vertical asymptote is at x= -4, so the domain is (-∞, -4) U (4, ∞)
The horizontal asymptote is at y = 0, so the range is (-∞, 0) U (0, ∞)
Blue graph is $\frac {1}{x}$
Green graph is $r(x) = \frac{1}{x+4}$
