Alright class, let's look at the given table and carefully construct a solution by mapping each [tex]\( x \)[/tex] value to its corresponding [tex]\( y \)[/tex] value. Here is our table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-6 & 3 \\
\hline
-5 & 0 \\
\hline
-2 & -3 \\
\hline
0 & -2 \\
\hline
1 & 0 \\
\hline
\end{array}
\][/tex]
### Step-by-Step Solution
1. Understanding the Problem:
We need to pair each [tex]\( x \)[/tex] value with its corresponding [tex]\( y \)[/tex] value and create a set of pairs.
2. Organize the Pairs:
We will start by listing out each [tex]\( x \)[/tex] value along with its [tex]\( y \)[/tex] value in the form of ordered pairs.
[tex]\[
\begin{array}{cc}
x = -6 & y = 3 \\
x = -5 & y = 0 \\
x = -2 & y = -3 \\
x = 0 & y = -2 \\
x = 1 & y = 0 \\
\end{array}
\][/tex]
3. Creating a Dictionary:
We represent these pairs in a dictionary or a mapping for clearer understanding.
- For [tex]\( x = -6 \)[/tex], [tex]\( y = 3 \)[/tex] can be represented as the pair (-6, 3).
- For [tex]\( x = -5 \)[/tex], [tex]\( y = 0 \)[/tex] can be represented as the pair (-5, 0).
- For [tex]\( x = -2 \)[/tex], [tex]\( y = -3 \)[/tex] can be represented as the pair (-2, -3).
- For [tex]\( x = 0 \)[/tex], [tex]\( y = -2 \)[/tex] can be represented as the pair (0, -2).
- For [tex]\( x = 1 \)[/tex], [tex]\( y = 0 \)[/tex] can be represented as the pair (1, 0).
4. Construct the Dictionary:
We now compile these pairs into a final form, which in mathematical terms can be written as:
[tex]\[
\{ (-6, 3), (-5, 0), (-2, -3), (0, -2), (1, 0) \}
\][/tex]
Or if we represent this information using a dictionary (which is a common data structure for such mappings):
[tex]\[
\{ -6: 3, -5: 0, -2: -3, 0: -2, 1: 0 \}
\][/tex]
### Final Answer:
The final result of mapping the given [tex]\( x \)[/tex] values to their corresponding [tex]\( y \)[/tex] values is:
[tex]\[
\{ -6: 3, -5: 0, -2: -3, 0: -2, 1: 0 \}
\][/tex]
This set of pairs or this dictionary accurately represents the relationship between the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values from the given table.
