To determine the range of the function, we need to examine the y-values in the table. The table of the function is provided as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 2 \\
\hline
2 & 4 \\
\hline
3 & 3 \\
\hline
4 & 2 \\
\hline
\end{array}
\][/tex]
The y-values from the table are: 2, 4, 3, and 2.
The range of a function is the set of all unique y-values that the function can output. To find this set, we need to list all distinct y-values from the table:
- From [tex]\(x = 1\)[/tex], [tex]\(y = 2\)[/tex]
- From [tex]\(x = 2\)[/tex], [tex]\(y = 4\)[/tex]
- From [tex]\(x = 3\)[/tex], [tex]\(y = 3\)[/tex]
- From [tex]\(x = 4\)[/tex], [tex]\(y = 2\)[/tex]
The unique y-values from the table are 2, 4, and 3.
Hence, the range of the function, which is the set of all unique y-values, is [tex]\(\{2, 3, 4\}\)[/tex].
Therefore, the correct answer is:
B. [tex]\(\{2, 3, 4\}\)[/tex]
