Use the table to answer the question.

Question

catogories are x, f(x), g(x).
x,-2,-1, 0, 1, 2
f(x),-1, 3/4, 1, 1 1/4, 3
g(x), 3, 3/4, 0, 3/4, 3
Compare the functions f(x)
and g(x)
. When is f(x)
greater than g(x)
?

(1 point)
Responses

−1<x<2
−1<x<2

−1<x<1
−1<x<1

−2<x<−1
−2<x<−1

−1<x<0

Answer 1

To compare the functions \( f(x) \) and \( g(x) \), we can examine their values at the given points in the table.

• 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 \( x = 1 \):

  • \( f(1) = 1\frac{1}{4} \) (or \( 1.25 \))
  • \( g(1) = \frac{3}{4} \)
  • \( f(1) > g(1) \)

• For \( x = 2 \):

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

Now, let’s summarize our comparison:

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

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

\[ 0 < x < 2 \]

However, carefully interpreting the intervals from the available options doesn't give us correct matches. The only ranges provided that encapsulate where \( f(x) > g(x) \) seem to overlap:

Valid outcome can be deduced as: \[ -1 < x < 2 \]

So, the final answer based on the choices given (since \( f(x) > g(x) \) starts at \( 0 \)) appears to correspond to:

−1 < x < 2