To compare the functions \( f(x) \) and \( g(x) \) using the provided data:
\[ \begin{array}{c|c|c} x & f(x) & g(x) \ \hline -2 & -1 & -1 \ -1 & 34 & 0 \ 0 & 1 & 1 \ 1 & 114 & 2 \ 2 & 3 & 3 \ \end{array} \]
Let's analyze the values of \( f(x) \) and \( g(x) \) for each given \( x \):
-
For \( x = -2 \):
- \( f(-2) = -1 \)
- \( g(-2) = -1 \)
- \( f(-2) \) is not greater than \( g(-2) \).
-
For \( x = -1 \):
- \( f(-1) = 34 \)
- \( g(-1) = 0 \)
- \( f(-1) \) is greater than \( g(-1) \).
-
For \( x = 0 \):
- \( f(0) = 1 \)
- \( g(0) = 1 \)
- \( f(0) \) is not greater than \( g(0) \).
-
For \( x = 1 \):
- \( f(1) = 114 \)
- \( g(1) = 2 \)
- \( f(1) \) is greater than \( g(1) \).
-
For \( x = 2 \):
- \( f(2) = 3 \)
- \( g(2) = 3 \)
- \( f(2) \) is not greater than \( g(2) \).
Summary:
- \( f(x) > g(x) \) when:
- \( x = -1 \)
- \( x = 1 \)
Therefore, \( f(x) \) is greater than \( g(x) \) for \( x = -1 \) and \( x = 1 \).