Using the table below, for what x-values is f(x) > g(x)?

Question

x f(x) g(x)
-2

7 -10
-1 4 -3
0 3 -2
1 4 -1
2 7 6
3 12 25
4 19 62


(1 point)
Responses

{7,4,3}
start set 7 comma 4 comma 3 end set

{−10,−3,−2,−1,6}
start set negative 10 comma negative 3 comma negative 2 comma negative 1 comma 6 end set

{−2,−1,0,1,2}
start set negative 2 comma negative 1 comma 0 comma 1 comma 2 end set

{12,19}

Answer 1

To determine the x-values for which \( f(x) > g(x) \), we need to compare the values of \( f(x) \) and \( g(x) \) for each x-value in the provided table.

Here's the provided data summarized for reference:

\[ \begin{array}{|c|c|c|} \hline x & f(x) & g(x) \ \hline -2 & 7 & -10 \ -1 & 4 & -3 \ 0 & 3 & -2 \ 1 & 4 & -1 \ 2 & 7 & 6 \ 3 & 12 & 25 \ 4 & 19 & 62 \ \hline \end{array} \]

Now, let's compare \( f(x) \) and \( g(x) \):

1. For \( x = -2 \): \( f(-2) = 7 \) and \( g(-2) = -10 \) → \( f(-2) > g(-2) \)
2. For \( x = -1 \): \( f(-1) = 4 \) and \( g(-1) = -3 \) → \( f(-1) > g(-1) \)
3. For \( x = 0 \): \( f(0) = 3 \) and \( g(0) = -2 \) → \( f(0) > g(0) \)
4. For \( x = 1 \): \( f(1) = 4 \) and \( g(1) = -1 \) → \( f(1) > g(1) \)
5. For \( x = 2 \): \( f(2) = 7 \) and \( g(2) = 6 \) → \( f(2) > g(2) \)
6. For \( x = 3 \): \( f(3) = 12 \) and \( g(3) = 25 \) → \( f(3) < g(3) \) (not included)
7. For \( x = 4 \): \( f(4) = 19 \) and \( g(4) = 62 \) → \( f(4) < g(4) \) (not included)

From this comparison, we see that \( f(x) > g(x) \) for the x-values: \( -2, -1, 0, 1, 2 \).

Therefore, the answer is: \[ \text{{\({-2, -1, 0, 1, 2}\)}} \]