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]
