To determine the transformation of \( f(x) \) that produces \( g(x) \), we can first analyze the values of both functions as given in the table.
Let's summarize the values:
\[ \begin{array}{c|c|c} x & f(x) & g(x) \ \hline -2 & 5 & 10 \ -1 & 2 & 4 \ 0 & 1 & 2 \ 1 & 2 & 4 \ 2 & 5 & 10 \ \end{array} \]
We can observe the relationship between \( f(x) \) and \( g(x) \):
- At \( x = -2 \), \( f(-2) = 5 \) results in \( g(-2) = 10 \) (which is \( 2 \cdot f(-2) \)).
- At \( x = -1 \), \( f(-1) = 2 \) results in \( g(-1) = 4 \) (which is \( 2 \cdot f(-1) \)).
- At \( x = 0 \), \( f(0) = 1 \) results in \( g(0) = 2 \) (which is \( 2 \cdot f(0) \)).
- At \( x = 1 \), \( f(1) = 2 \) results in \( g(1) = 4 \) (which is \( 2 \cdot f(1) \)).
- At \( x = 2 \), \( f(2) = 5 \) results in \( g(2) = 10 \) (which is \( 2 \cdot f(2) \)).
From this pattern, we can conclude that \( g(x) \) is simply \( 2 \) times \( f(x) \).
Thus, the transformation is:
\[ g(x) = 2f(x) \]
Answer: \( g(x) = 2f(x) \)