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)
?

(1 point)
f(x)
is greater than g(x)
when
<x<

Answer 1

To compare the functions \( f(x) \) and \( g(x) \) based on the provided values in the table:

| \( x \) | \( f(x) \) | \( g(x) \) |
|-----|--------|--------|
| -2 | -1 | -1 |
| -1 | 34 | 0 |
| 0 | 1 | 1 |
| 1 | 114 | 2 |
| 2 | 3 | 3 |

Now, let's compare \( f(x) \) and \( g(x) \):

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 \( g(2) \).

Based on the comparisons:

- \( f(x) > g(x) \) when \( x = -1 \) and \( x = 1 \).

Thus, the answer is:
**f(x) is greater than g(x) when \( -1 < x < 2 \) (taking into account that it does not hold exactly at 2).**