Answered

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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]

Range: {0, 2, 4}

Sagot :

GinnyAnswer
To determine the range of the relation given in the table, we need to focus on the [tex]\( y \)[/tex]-values because the range of a function or relation is the set of all possible [tex]\( y \)[/tex]-values (outputs).

Here are the given pairs from the table along with their respective [tex]\( y \)[/tex]-values:

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

From the table, the [tex]\( y \)[/tex]-values are:

[tex]\[ y = 0, 2, 4, 2, 0 \][/tex]

Notice that some [tex]\( y \)[/tex]-values are repeated. We need the set of unique [tex]\( y \)[/tex]-values to determine the range. So, we list each [tex]\( y \)[/tex]-value without repetition:

[tex]\[ \{0, 2, 4\} \][/tex]

Finally, we can also arrange these values in ascending order to present the range in a standard format:

[tex]\[ \{0, 2, 4\} \][/tex]

Therefore, the range of the relation is:

[tex]\[ \{0, 2, 4\} \][/tex]
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