Question

Use the table to answer the question.
x f(x) g(x)
-2 -1 -1
-1 3/4 0
0 1 1
1 1 1/4 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 \( g(x) \) from the table, we analyze the values of both functions at given points:

- For \( x = -2 \): \( f(-2) = -1 \), \( g(-2) = -1 \) → \( f(x) = g(x) \)
- For \( x = -1 \): \( f(-1) = \frac{3}{4} \), \( g(-1) = 0 \) → \( f(x) > g(x) \)
- For \( x = 0 \): \( f(0) = 1 \), \( g(0) = 1 \) → \( f(x) = g(x) \)
- For \( x = 1 \): \( f(1) = 1 \), \( g(1) = \frac{1}{4} \) → \( f(x) > g(x) \)
- For \( x = 2 \): \( f(2) = 3 \), \( g(2) = 3 \) → \( f(x) = g(x) \)

From this analysis, we can summarize:

- \( f(x) \) is greater than \( g(x) \) in the intervals:
- Between \( x = -1 \) and \( x = 0 \) (specifically \( -1 < x < 0 \))
- At \( x = 1 \), \( f(x) > g(x) \)

Thus, we can conclude that \( f(x) \) is greater than \( g(x) \) when:

**f(x) is greater than g(x) when -1 < x < 2.**