Answer
Domain: (-∞, 4) U (4, ∞)
Range: (-∞, 2) U (2, ∞)
See graph below
Work Step by Step
The question asks for a graph of the function and the function's domain and range.
Given $r(x) = \frac{2x-9}{x-4}$
By dividing the function, $r(x) = 2 - \frac{1}{x-4}$
From $\frac{1}{x}$, the graph is transformed four units to the right, reflected about the x-axis, then shifted up two units
The vertical asymptote is at x= 4, so the domain is (-∞, 4) U (4, ∞)
The horizontal asymptote is at y = 2, so the range is (-∞, 2) U (2, ∞)
Blue graph is $\frac {1}{x}$
Green graph is $r(x) = \frac{2x-9}{x-4}$
