To determine how many units the function \( f(x) \) is horizontally translated to form \( g(x) \), we can identify corresponding points from both functions.
From the table for \( f(x) \), we have:
- \( f(0) = 1 \)
- \( f(1) = 2 \)
- \( f(2) = 9 \)
From the table for \( g(x) \), we have:
- \( g(3) = 0 \)
- \( g(4) = 1 \)
- \( g(5) = 2 \)
- \( g(6) = 9 \)
To find the translation, we look for corresponding values of \( f(x) \) and \( g(x) \):
- \( f(0) = 1 \) corresponds to \( g(4) = 1 \): Here, \( 0 + 4 = 4 \).
- \( f(1) = 2 \) corresponds to \( g(5) = 2 \): Here, \( 1 + 4 = 5 \).
- \( f(2) = 9 \) corresponds to \( g(6) = 9 \): Here, \( 2 + 4 = 6 \).
In all cases, each \( x \) value in \( f(x) \) is shifted by \( 4 \) units to produce the corresponding \( x \) value in \( g(x) \).
Thus, the original function has been translated by 4 units.