Answer :

Look carefully. You can see that the vertical asymptote of the original function has been moved 5 units to the right, and the horiz. asy. 3 units down.

Thus, the function in question is g(x) = 2
------- - 3
x-5

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Rewritten by : Barada

The translated graph of the core function y = 2/x can be represented by the equation f(x) = 2/(x-h) for horizontal shifts, or f(x) = 2/x + k for vertical shifts, where 'h' and 'k' are the magnitudes of the shifts. Without details on the shift's direction and magnitude, we cannot provide an exact equation.

To determine the function that represents a translation of the core graph y = 2/x, we need to look at the shifts applied to the original graph. The question implies that the graph has been shifted either horizontally or vertically. A horizontal shift to the right by 'h' units would result in the equation f(x) = 2/(x-h). A vertical shift upwards by 'k' units would lead to the equation f(x) = 2/x + k. Without specific information about the direction or magnitude of the shift, we cannot provide an exact equation, but these forms will describe the transformed function.

To verify that the transformation is correct, one could check critical points such as x-intercepts and y-intercepts and ensure they have moved according to the described transformations. For example, if the graph has moved 2 units to the right, the equation of the new function would be f(x) = 2/(x-2).

Therefore, the equation of a translated function based on the core graph y = 2/x can be defined as f(x) = 2/(x-h) for horizontal shifts or f(x) = 2/x + k for vertical shifts, where 'h' and 'k' are the magnitudes of the horizontal and vertical shifts, respectively.