Question

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 3Compare the functions f(x)
and g(x)
. When is g(x)
greater than f(x)
?(1 point)
g(x)
is greater than f(x)
when x<
.

Answer 1

To compare the functions \( f(x) \) and \( g(x) \) based on the values provided in the table:

\[ \begin{array}{|c|c|c|} \hline x & f(x) & g(x) \ \hline -2 & -1 & 3 \ -1 & 34 & 34 \ 0 & 1 & 0 \ 1 & 114 & 34 \ 2 & 3 & 3 \ \hline \end{array} \]

Now we analyze whether \( g(x) \) is greater than \( f(x) \) for each value of \( x \):

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

Based on the analysis, \( g(x) \) is greater than \( f(x) \) only when \( x < -1 \).

So, the final answer is: \( g(x) \) is greater than \( f(x) \) when \( x < -1 \).