The equation \( y = f(x - 3) \) represents a horizontal translation of the function \( y = f(x) \). Specifically, this transformation shifts the graph of the function to the right by 3 units.
To clarify:
- If you have the original function \( y = f(x) \) and you replace \( x \) with \( (x - 3) \), it effectively means that for every \( x \) value in the original function, you are now using \( x - 3 \) as the input.
- This means that for any given output value \( y \) in the original function, you now need to go 3 units to the right to get the same output value in the transformed function.
Thus, the translation is to the right, not left. If it were \( y = f(x + 3) \), that would be a translation to the left by 3 units.