Let's solve each part of the question step-by-step using the given table of values.
The table of values is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
-3 & 33 \\
\hline
-2 & 17 \\
\hline
0 & -15 \\
\hline
2 & -7 \\
\hline
3 & 27 \\
\hline
\end{tabular}
\][/tex]
1. Find [tex]\( f(0) \)[/tex]
To find [tex]\( f(0) \)[/tex], we need to look at the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex]:
From the table:
[tex]\[
x = 0 \implies f(x) = -15
\][/tex]
So, [tex]\( f(0) = -15 \)[/tex].
2. Find [tex]\( x \)[/tex] when [tex]\( f(x) = 27 \)[/tex]
To find the value of [tex]\( x \)[/tex] when [tex]\( f(x) = 27 \)[/tex], we need to look for the row in the table where [tex]\( f(x) \)[/tex] is 27:
From the table:
[tex]\[
f(x) = 27 \implies x = 3
\][/tex]
So, when [tex]\( f(x) = 27 \)[/tex], [tex]\( x = 3 \)[/tex].
Combining both parts, the answers are:
- [tex]\( f(0) = -15 \)[/tex]
- When [tex]\( f(x) = 27 \)[/tex], [tex]\( x = 3 \)[/tex]
