The transformation \( f(x) \mapsto f(x - 2) \) represents a horizontal shift of the graph of the function \( f(x) \).
Specifically, this transformation shifts the graph of \( f(x) \) to the right by 2 units.
Here's why this happens:
- The expression \( f(x - 2) \) means that for any value of \( x \), you are evaluating the function at a point that is 2 units to the left of where you would normally evaluate it (because you are subtracting 2 from \( x \)).
- Therefore, to achieve the same output (i.e., the same y-value) from \( f(x) \), you need to use an input that is 2 units larger than \( x \) in the original function, meaning the entire graph shifts to the right.
In summary, the transformation \( f(x) \mapsto f(x - 2) \) shifts the graph of \( f(x) \) 2 units to the right.
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