Question

Which of the following statements describes the transformation indicated by
f(x)=x^2 becomes g(x)=(x-3)^2
Function f was translated horizontally 3 units to left
Vertically 3 units down
Horizontally 3 units to right
Vertically 3 up

Answer 1

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.**