Answer:
We can use the transformations of the graph of y=1/x to graph the rational function r(x) = 2x-9/x-4.
First, we will shift the graph of y=1/x to the right by 4 units to get the graph of y=1/(x-4). Next, we will stretch the graph vertically by a factor of 2 to get the graph of y=2/(x-4). Finally, we will shift the graph down by 9 units to get the graph of r(x) = 2x-9/x-4.
The domain of r(x) is all real numbers except x=4, since that would make the denominator zero. The range of r(x) is also all real numbers except y=2, since that would make the numerator zero.
Here is a rough sketch of the graph of r(x), using the transformations:
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x=4 y=2
Note: This graph is not to scale and is intended to show the general shape of the graph.