Answer the following two questions. Use commas to separate your answers.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline \multicolumn{11}{|c|}{ Evaluating Functions } \\
\hline \multicolumn{11}{|c|}{ Use the table to answer the following questions } \\
\hline [tex]$x$[/tex] & 0 & 3 & 6 & 9 & 12 & 15 & 18 & 21 & 24 & 27 \\
\hline [tex]$f(x)$[/tex] & 15 & 24 & 18 & 12 & 21 & 9 & 0 & 6 & 3 & 27 \\
\hline
\end{tabular}

\begin{tabular}{|c|l|}
\hline Evaluate [tex]$f(6):$[/tex] & [tex]$f(6)=\square$[/tex] \\
\hline Determine [tex]$x$[/tex] when [tex]$f(x)=21$[/tex] & [tex]$x=\square$[/tex] \\
\hline
\end{tabular}



Answer :

Let’s carefully analyze the given table to answer the two questions.

Here’s the table with \( x \) and \( f(x) \) values:

[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline x & 0 & 3 & 6 & 9 & 12 & 15 & 18 & 21 & 24 & 27 \\ \hline f(x) & 15 & 24 & 18 & 12 & 21 & 9 & 0 & 6 & 3 & 27 \\ \hline \end{array} \][/tex]

1. Evaluate \( f(6) \):
- To find \( f(6) \), we need to look at the value under \( f(x) \) where \( x = 6 \).
- From the table, when \( x = 6 \), \( f(x) = 18 \).

So, \( f(6) = 18 \).

2. Determine \( x \) when \( f(x) = 21 \):
- To find the value of \( x \) when \( f(x) = 21 \), we need to locate the \( x \) value corresponding to \( f(x) = 21 \).
- From the table, when \( f(x) = 21 \), the corresponding \( x \) value is \( 12 \).

Therefore, \( x = 12 \) when \( f(x) = 21 \).

Thus, the answers are:

[tex]\[ f(6) = 18, \, x = 12 \][/tex]

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