Let's start by understanding the problem and the given elements in a clear and concise manner.
1. Ordered Pairs:
The problem provides a set of ordered pairs:
[tex]\[
\{(-3,5),(-1,2),(1,-1),(-1,4)\}
\][/tex]
These ordered pairs essentially show how each [tex]\( x \)[/tex] value maps to a specific [tex]\( y \)[/tex] value.
2. Table Representation:
To better visualize and understand these mappings, we can represent them in a tabular form where the first column lists the [tex]\( x \)[/tex] values and the second column lists the corresponding [tex]\( y \)[/tex] values:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-3 & 5 \\
\hline
-1 & 2 \\
\hline
1 & -1 \\
\hline
-1 & 4 \\
\hline
\end{tabular}
\][/tex]
This table format helps us see the mappings clearly.
3. Structure of the Ordering and Representation (Mapping Diagram):
We'll consider the mapping diagram, which is another way to visualize the relationship between the [tex]\( x \)[/tex] values and the [tex]\( y \)[/tex] values.
The mapping diagram can be represented as two columns:
- One for [tex]\( x \)[/tex] values: [tex]\( \{-3, -1, 1, -1\} \)[/tex]
- One for [tex]\( y \)[/tex] values: [tex]\( \{5, 2, -1, 4\} \)[/tex]
Each [tex]\( x \)[/tex] value will have an arrow pointing to its corresponding [tex]\( y \)[/tex] value, showing the exact mapping between the two sets.
In summary:
1. The set of ordered pairs is:
[tex]\[
\{(-3, 5), (-1, 2), (1, -1), (-1, 4)\}
\][/tex]
2. The table of the mappings is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-3 & 5 \\
\hline
-1 & 2 \\
\hline
1 & -1 \\
\hline
-1 & 4 \\
\hline
\end{tabular}
\][/tex]
This provides a clear representation of the given information and ensures that the problem is well understood.
