To understand the transformation from the function \( f(x) = x^2 \) to \( g(x) = (x - 3)^2 \), we need to analyze the change made to the function.
The general form of a horizontal translation can be described as follows:
- \( g(x) = f(x - h) \) translates the function \( f(x) \) horizontally to the right by \( h \) units if \( h \) is positive.
- \( g(x) = f(x + h) \) translates the function \( f(x) \) horizontally to the left by \( h \) units if \( h \) is negative.
In this case, we have \( g(x) = (x - 3)^2 \), which can be written in the form of \( f(x) \) by recognizing that \( (x - 3) \) shifts the entire function \( f(x) \) horizontally:
- The function \( f(x) = x^2 \) has been changed to \( g(x) = (x - 3)^2 \), meaning that the function has been shifted to the right by 3 units.
Therefore, the correct statement is:
**Horizontally 3 units to the right.**