Question

se 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


(1 point)
Compare the functions f(x)
and g(x)

When is f(x)
greater than g(x)
?

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

Answer 1

To determine when \( f(x) \) is greater than \( g(x) \), let's analyze the values from the table:

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

From the table we can extract the following comparisons:
- At \( x = -2 \): \( f(x) = -1 \) and \( g(x) = -1 \) → \( f(x) \) is not greater.
- At \( x = -1 \): \( f(x) = 34 \) and \( g(x) \) is not defined → \( f(x) \) is greater.
- At \( x = 0 \): \( f(x) = 1 \) and \( g(x) = 1 \) → \( f(x) \) is not greater.
- At \( x = 1 \): \( f(x) \) is not defined and \( g(x) = 114 \) → \( f(x) \) cannot be compared.
- At \( x = 2 \): \( f(x) = 3 \) and \( g(x) = 3 \) → \( f(x) \) is not greater.

From this analysis, we can see that \( f(x) \) is greater than \( g(x) \) only at \( x = -1 \).

Thus, we conclude:
- \( f(x) \) is greater than \( g(x) \) when \( -1 < x < 0 \).

So we can say:

\( f(x) \) is greater than \( g(x) \) when
\[
-1 < x < 0
\]