Your explanation is on the right track, but there seems to be a slight confusion in your description.
For the graph of =()−2y=f(x)−2, the graph of =()y=f(x) is shifted downward by 2 units. This means that every point on the graph of ()f(x) is lowered by 2 units.
For the graph of =(−2)y=f(x−2), the graph of =()y=f(x) is shifted to the right by 2 units. This means that every point on the graph of ()f(x) is shifted horizontally to the right by 2 units.
So, in summary:
- =()−2y=f(x)−2 shifts the graph of ()f(x) downward by 2 units.
- =(−2)y=f(x−2) shifts the graph of ()f(x) to the right by 2 units.
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