Use the table to answer the question.

Question

x f(x) g(x)
−2 −1 3
−1 3/4 3/4
0 1 0
1 1 1/4 3/4
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 will compare the values of \( f(x) \) and \( g(x) \) from the table.

Let's list the values for \( f(x) \) and \( g(x) \):

• For \( x = -2 \):

  • \( f(-2) = -1 \)
  • \( g(-2) = 3 \)
  • \( f(-2) < g(-2) \)

• For \( x = -1 \):

  • \( f(-1) = \frac{3}{4} \)
  • \( g(-1) = \frac{3}{4} \)
  • \( f(-1) = g(-1) \)

• For \( x = 0 \):

  • \( f(0) = 1 \)
  • \( g(0) = 0 \)
  • \( f(0) > g(0) \)

• For \( x = 1 \):

  • \( f(1) = \frac{5}{4} \)
  • \( g(1) = \frac{3}{4} \)
  • \( f(1) > g(1) \)

• For \( x = 2 \):

  • \( f(2) = 3 \)
  • \( g(2) = 3 \)
  • \( f(2) = g(2) \)

From this analysis, we see that:

• \( f(x) < g(x) \) for \( x = -2 \)
• \( f(x) = g(x) \) for \( x = -1 \) and \( x = 2 \)
• \( f(x) > g(x) \) for \( x = 0 \) and \( x = 1 \)

Thus, \( f(x) \) is greater than \( g(x) \) in the interval:

\[ 0 < x < 1 \]

So the final answer is:

f(x) is greater than g(x) when \( 0 < x < 1 \).