Question

Use the table to answer the question.

x f(x)
g(x)

−2
−1
−1

−1
34
0
0 1 1
1 114
2
2 3 3
Compare the functions f(x)
and g(x)
. When is f(x)
greater than g(x)
?

Answer 1

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 \( x \):

1. **For \( x = -2 \)**:
- \( f(-2) = -1 \)
- \( g(-2) = -1 \)
- \( f(-2) \) is not greater than \( g(-2) \).

2. **For \( x = -1 \)**:
- \( f(-1) = 34 \)
- \( g(-1) = 0 \)
- \( f(-1) \) is greater than \( g(-1) \).

3. **For \( x = 0 \)**:
- \( f(0) = 1 \)
- \( g(0) = 1 \)
- \( f(0) \) is not greater than \( g(0) \).

4. **For \( x = 1 \)**:
- \( f(1) = 114 \)
- \( g(1) = 2 \)
- \( f(1) \) is greater than \( g(1) \).

5. **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 \( x = 1 \).