Question

Use the table to answer the question.

x f(x)
g(x)

−2
−1
3
−1
34
34

0 1 0
1 114
34

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 determine when \( f(x) \) is greater than \( g(x) \), we can analyze the values provided in the table.

From the table, we can extract the following values:

- At \( x = -2 \):
- \( f(x) = -1 \)
- \( g(x) = 3 \)

- At \( x = -1 \):
- \( f(x) = 34 \)
- \( g(x) = 34 \)

- At \( x = 0 \):
- \( f(x) = 1 \)
- \( g(x) = 0 \)

- At \( x = 1 \):
- \( f(x) = 114 \)
- \( g(x) = 34 \)

- At \( x = 2 \):
- \( f(x) = 3 \)
- \( g(x) = 3 \)

Now let's compare \( f(x) \) and \( g(x) \) at these points:

- For \( x = -2 \): \( f(-2) = -1 < g(-2) = 3 \)
- For \( x = -1 \): \( f(-1) = 34 = g(-1) = 34 \)
- For \( x = 0 \): \( f(0) = 1 > g(0) = 0 \)
- For \( x = 1 \): \( f(1) = 114 > g(1) = 34 \)
- For \( x = 2 \): \( f(2) = 3 = g(2) = 3 \)

From this analysis, we find that \( f(x) \) is greater than \( g(x) \) when \( x \) is in the intervals:

- \( x = 0 \) (where \( f(0) > g(0) \))
- \( x = 1 \) (where \( f(1) > g(1) \))

Thus, the only segments where \( f(x) > g(x) \) are when \( x \) is in the range \( 0 < x < 1 \).

So, we can conclude:

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

\[
\boxed{0 < x < 1}
\]