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

[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
$x$ & 0 & 5 & 10 & 15 \\
\hline
$y$ & 1 & 7 & 9 & 2 \\
\hline
\end{tabular}
\][/tex]

A. [tex]\(x \geq 0\)[/tex]
B. [tex]\(y \geq 1\)[/tex]
C. [tex]\(\{0, 5, 10, 15\}\)[/tex]
D. [tex]\(\{1, 2, 7, 9\}\)[/tex]


Sagot :

To find the range of the relation shown in your table, we need to extract the possible output values, which are the [tex]\( y \)[/tex]-values. Let's look at the [tex]\( y \)[/tex]-values given in your table:

[tex]\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 5 & 10 & 15 \\ \hline y & 1 & 7 & 9 & 2 \\ \hline \end{array} \][/tex]

The [tex]\( y \)[/tex]-values provided are:

[tex]\[ y = 1, 7, 9, 2 \][/tex]

The range of a relation is the set of all different [tex]\( y \)[/tex]-values. To determine this, we will list each unique [tex]\( y \)[/tex]-value from the table. Here we have:

[tex]\[ 1, 7, 9, 2 \][/tex]

Thus, the range of the relation consists of these values. Arranging them in a set (and typically we list set elements in ascending order, although it's not required):

[tex]\[ \{1, 2, 7, 9\} \][/tex]

However, since there is no need to sort in this context, the range can also be presented exactly as we find them:

[tex]\[ \{1, 7, 9, 2\} \][/tex]

Therefore, the range of the relation is:

[tex]\[ \{1, 7, 9, 2\} \][/tex]

This is the set of all outputs [tex]\( y \)[/tex]-values for the given inputs [tex]\( x \)[/tex].
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