Sure! Let's go through the problem step-by-step by using the table you provided.
The table lists values of [tex]\( x \)[/tex] and their corresponding function values [tex]\( f(x) \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & -7 \\
-1 & -4 \\
0 & -1 \\
1 & 2 \\
2 & 5 \\
\hline
\end{array}
\][/tex]
Our goal is to extract the [tex]\( x \)[/tex] values and the corresponding [tex]\( f(x) \)[/tex] values.
### Step-by-Step Solution:
1. Identify the [tex]\( x \)[/tex] values:
The [tex]\( x \)[/tex] values in the table are:
[tex]\[
x = \{-2, -1, 0, 1, 2\}
\][/tex]
2. Identify the [tex]\( f(x) \)[/tex] values:
The [tex]\( f(x) \)[/tex] values corresponding to each [tex]\( x \)[/tex] value are:
[tex]\[
f(x) = \{-7, -4, -1, 2, 5\}
\][/tex]
### Summary of Results:
- List of [tex]\( x \)[/tex] values: [tex]\([-2, -1, 0, 1, 2]\)[/tex]
- List of [tex]\( f(x) \)[/tex] values: [tex]\([-7, -4, -1, 2, 5]\)[/tex]
Upon review, we see that the pairs [tex]\((x, f(x))\)[/tex] perfectly correspond to the values in the table provided:
- For [tex]\( x = -2 \)[/tex], [tex]\( f(x) = -7 \)[/tex]
- For [tex]\( x = -1 \)[/tex], [tex]\( f(x) = -4 \)[/tex]
- For [tex]\( x = 0 \)[/tex], [tex]\( f(x) = -1 \)[/tex]
- For [tex]\( x = 1 \)[/tex], [tex]\( f(x) = 2 \)[/tex]
- For [tex]\( x = 2 \)[/tex], [tex]\( f(x) = 5 \)[/tex]
Therefore, the tables summarizing the [tex]\( x \)[/tex] values and the corresponding [tex]\( f(x) \)[/tex] values are as follows:
[tex]\[
\begin{array}{ccc}
x & : & \{-2, -1, 0, 1, 2\} \\
f(x) & : & \{-7, -4, -1, 2, 5\}
\end{array}
\][/tex]
This detail confirms the correspondence between the values in a clear and systematic manner.
