What is the range of the relation in the table below?

[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-2 & 0 \\
\hline
-1 & 2 \\
\hline
0 & 4 \\
\hline
1 & 2 \\
\hline
2 & 0 \\
\hline
\end{tabular}
\][/tex]

A. range: [tex]$\{0, 2, 4\}$[/tex]
B. range: [tex]$\{0, 4\}$[/tex]
C. range: [tex]$\{-2, -1, 0, 1, 2\}$[/tex]
D. range: [tex]$\{0, 2\}$[/tex]



Answer :

To determine the range of the given relation, let's follow these steps:

1. Identify the Set of [tex]\(y\)[/tex]-Values:
From the table, the [tex]\(y\)[/tex]-values associated with each [tex]\(x\)[/tex]-value are:
[tex]\[ \begin{aligned} y & = 0 \quad \text{(when \(x = -2\))}, \\ y & = 2 \quad \text{(when \(x = -1\))}, \\ y & = 4 \quad \text{(when \(x = 0\))}, \\ y & = 2 \quad \text{(when \(x = 1\))}, \\ y & = 0 \quad \text{(when \(x = 2\))}. \end{aligned} \][/tex]

2. Determine the Unique [tex]\(y\)[/tex]-Values:
Write down the [tex]\(y\)[/tex]-values from the above list:
[tex]\[ \{0, 2, 4, 2, 0\} \][/tex]
Notice that there are duplicates in this list. To identify the unique [tex]\(y\)[/tex]-values, we remove the duplicates, leaving us with:
[tex]\[ \{0, 2, 4\} \][/tex]

3. State the Range:
The range of the relation is the set of all unique [tex]\(y\)[/tex]-values from the table. Thus, the range is:
[tex]\[ \{0, 2, 4\} \][/tex]

Given the answer provided earlier and the choices listed, the correct choice is:
[tex]\[ \text{range: } \{0, 2, 4\} \][/tex]