To determine the transformation described by the functions \( f(x) = x^2 \) and \( g(x) = (x-3) \), we need to analyze how \( g(x) \) modifies \( f(x) \).
The function \( f(x) = x^2 \) represents a standard parabola that opens upwards. The function \( g(x) = (x - 3) \) indicates a horizontal shift.
In general, when you see a transformation like \( f(x - h) \), it involves shifting the graph of \( f(x) \) horizontally:
- If \( h > 0 \), the graph shifts to the right.
- If \( h < 0 \), the graph shifts to the left.
In this case, \( g(x) = (x - 3) \) suggests that the transformation performed is \( f(x - 3) \), which means the function \( f(x) \) is shifted 3 units to the right.
Thus, the correct statement that describes the transformation is:
Function \( f \) was translated (shifted) horizontally 3 units to the right.
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