To determine how many units the function \( f(x) \) is horizontally translated to become \( g(x) \), we need to examine the values of \( x \) in both functions.
Looking at the tables:
For \( f(x) \):
- \( f(-1) = 0 \)
- \( f(0) = 1 \)
- \( f(1) = 2 \)
- \( f(2) = 9 \)
For \( g(x) \):
- \( g(3) = 0 \)
- \( g(4) = 1 \)
- \( g(5) = 2 \)
- \( g(6) = 9 \)
Now, let's analyze how the \( x \)-values correspond to each other.
From the table:
- The input value for \( g(3) = 0 \) which corresponds to \( f(-1) = 0 \).
- The input value for \( g(4) = 1 \) corresponds to \( f(0) = 1 \).
- The input value for \( g(5) = 2 \) corresponds to \( f(1) = 2 \).
- The input value for \( g(6) = 9 \) corresponds to \( f(2) = 9 \).
From the mapping, we can see that:
- The input values of \( f(x) \) (−1, 0, 1, 2) are now found in \( g(x) \) at positions (3, 4, 5, 6).
To find the translation, we observe that the lowest \( x \) value from \( f(x) \) is -1 and the lowest \( x \) value from \( g(x) \) is 3.
To determine how many units \( f(x) \) has been translated, we can calculate:
\[ 3 - (-1) = 3 + 1 = 4. \]
Thus, the original function has been translated by 4 units.
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