Final answer:
The equation of the graph obtained by shrinking the graph of y = 1/x horizontally by a factor of 6 and shifting it down 9 units is y = 1/(6x) - 9.
Step-by-step explanation:
The student is asking for the equation of a graph that results from applying transformations to the function y = 1/x. Specifically, the graph is to be shrunk horizontally by a factor of 6 and shifted downwards by 9 units.
To shrink the graph of y = 1/x horizontally by a factor of 6, we multiply the x variable by 6. This operation is reflected in the function's equation by transforming it to y = 1/(6x). Next, to shift the graph downwards by 9 units, we subtract 9 from the entire function, which modifies the equation to y = 1/(6x) - 9.
This is the equation of the desired graph after applying the specified transformations. It's critical to understand how horizontal shrink and vertical shifts affect the equation of a function.