To sketch the given equations, we will start with the graph of the original function f(x) = 2/(x-2) + 2 and then apply the necessary transformations.
1. y = f(x-2):
To sketch y = f(x-2), we need to shift the graph of f(x) two units to the right. This can be done by replacing x in the equation f(x) with (x-2). The equation becomes y = f(x-2) = 2/((x-2)-2) + 2 = 2/(x-4) + 2.
2. y = f(x-1) - 3:
To sketch y = f(x-1) - 3, we need to shift the graph of f(x) one unit to the right and three units downward. This can be done by replacing x in the equation f(x) with (x-1) and subtracting 3 from the result. The equation becomes y = f(x-1) - 3 = 2/((x-1)-2) + 2 - 3 = 2/(x-3) - 1.
Now, let's plot these equations on a graph:
Note: The graph of the original function f(x) = 2/(x-2) + 2 should be sketched first before applying the transformations.
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